Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

$log subscript 4 end subscript invisible function application 18$ is

A rational number
An irrational number
A prime number
None of these

The correct answer is: An irrational number

Let $log subscript 4 end subscript invisible function application 18 equals p divided by q comma blank w h e r e blank p comma q element of I$
$rightwards double arrow log subscript 4 end subscript invisible function application 9 plus log subscript 4 end subscript invisible function application 2 equals fraction numerator p over denominator q end fraction rightwards double arrow fraction numerator 1 over denominator 2 end fraction cross times 2 log subscript 2 end subscript invisible function application 3 plus fraction numerator 1 over denominator 2 end fraction equals fraction numerator p over denominator q end fraction rightwards double arrow log subscript 2 end subscript invisible function application 3 equals fraction numerator p over denominator q end fraction minus fraction numerator 1 over denominator 2 end fraction equals fraction numerator m over denominator n end fraction open parentheses s a y close parentheses$
Where $m comma blank n element of I blank a n d blank n not equal to 0 rightwards double arrow 3 equals open parentheses 2 close parentheses to the power of m divided by n end exponent rightwards double arrow 3 to the power of n end exponent equals 2 to the power of m end exponent$ (possible only when $m equals n equals 0$ which is not true)
Hence, $log subscript 4 end subscript invisible function application 18$ is an irrational number

Related Questions to study

If $sin invisible function application 6 theta plus sin invisible function application 4 theta plus sin invisible function application 2 theta equals 0 comma$ then $theta blank$ is equal to $blank open parentheses n element of Z close parentheses$

If $sin invisible function application 6 theta plus sin invisible function application 4 theta plus sin invisible function application 2 theta equals 0 comma$ then $theta blank$ is equal to $blank open parentheses n element of Z close parentheses$

The area of the circle and the area of a regular polygon of $n$ sides and of perimeter equal to that of the circle are in the ratio of

The area of the circle and the area of a regular polygon of $n$ sides and of perimeter equal to that of the circle are in the ratio of

$I f blank x element of open parentheses pi comma fraction numerator 3 pi over denominator 2 end fraction close parentheses comma blank t h e n blank 4 cos to the power of 2 end exponent invisible function application open parentheses fraction numerator pi over denominator 4 end fraction minus fraction numerator x over denominator 2 end fraction close parentheses plus square root of 4 sin to the power of 4 end exponent invisible function application x plus sin to the power of 2 end exponent invisible function application 2 x end root$ is always equal to

$I f blank x element of open parentheses pi comma fraction numerator 3 pi over denominator 2 end fraction close parentheses comma blank t h e n blank 4 cos to the power of 2 end exponent invisible function application open parentheses fraction numerator pi over denominator 4 end fraction minus fraction numerator x over denominator 2 end fraction close parentheses plus square root of 4 sin to the power of 4 end exponent invisible function application x plus sin to the power of 2 end exponent invisible function application 2 x end root$ is always equal to

parallel

If $tan invisible function application theta plus sin invisible function application theta equals m blank a n d tan invisible function application theta minus sin invisible function application theta equals n comma$ then

If $tan invisible function application theta plus sin invisible function application theta equals m blank a n d tan invisible function application theta minus sin invisible function application theta equals n comma$ then

$I f blank x subscript 1 end subscript blank a n d blank x subscript 2 end subscript$ are two distinct roots of the equation $a cos invisible function application x plus b sin invisible function application x equals c comma blank t h e n tan invisible function application fraction numerator x subscript 1 end subscript plus x subscript 2 end subscript over denominator 2 end fraction$ is equal to

$I f blank x subscript 1 end subscript blank a n d blank x subscript 2 end subscript$ are two distinct roots of the equation $a cos invisible function application x plus b sin invisible function application x equals c comma blank t h e n tan invisible function application fraction numerator x subscript 1 end subscript plus x subscript 2 end subscript over denominator 2 end fraction$ is equal to

$I f fraction numerator sin invisible function application open parentheses x plus y close parentheses over denominator sin invisible function application open parentheses x minus y close parentheses end fraction equals fraction numerator a plus b over denominator a minus b end fraction comma blank t h e n fraction numerator tan invisible function application x over denominator tan invisible function application y end fraction blank i s blank e q u a l blank t o$

$I f fraction numerator sin invisible function application open parentheses x plus y close parentheses over denominator sin invisible function application open parentheses x minus y close parentheses end fraction equals fraction numerator a plus b over denominator a minus b end fraction comma blank t h e n fraction numerator tan invisible function application x over denominator tan invisible function application y end fraction blank i s blank e q u a l blank t o$

parallel

Which of the following is not the general solution of $2 to the power of cos invisible function application 2 x end exponent plus 1 equals 3.2 to the power of negative sin to the power of 2 end exponent invisible function application x end exponent ?$

Which of the following is not the general solution of $2 to the power of cos invisible function application 2 x end exponent plus 1 equals 3.2 to the power of negative sin to the power of 2 end exponent invisible function application x end exponent ?$

In triangle $A B C comma$ base $B C$ and area of triangle $increment$ are fixed. Locus of the centroid of triangle $A B C$ is a straight line that is

In triangle $A B C comma$ base $B C$ and area of triangle $increment$ are fixed. Locus of the centroid of triangle $A B C$ is a straight line that is

The radii $r subscript 1 end subscript comma blank r subscript 2 end subscript comma blank r subscript 3 end subscript$ of the escribed circles of the triangle $A B C$ are in H.P. If the area of the triangle is 24 $c m to the power of 2 end exponent$ and its perimeter is 24 cm, then the length of its largest side is

The radii $r subscript 1 end subscript comma blank r subscript 2 end subscript comma blank r subscript 3 end subscript$ of the escribed circles of the triangle $A B C$ are in H.P. If the area of the triangle is 24 $c m to the power of 2 end exponent$ and its perimeter is 24 cm, then the length of its largest side is

parallel

In an acute angled triangle $A B C comma blank r plus r subscript 1 end subscript equals r subscript 2 end subscript plus r subscript 3 end subscript blank$ and $blank angle B greater than fraction numerator pi over denominator 3 end fraction comma$ then

In an acute angled triangle $A B C comma blank r plus r subscript 1 end subscript equals r subscript 2 end subscript plus r subscript 3 end subscript blank$ and $blank angle B greater than fraction numerator pi over denominator 3 end fraction comma$ then

If $´ O ´$ is the circumcentre of $increment A B C blank$ and $blank R subscript 1 end subscript comma R subscript 2 end subscript blank$ and $blank R subscript 3 end subscript$ are the radii of the circumcircles of triangles $O B C comma blank O C A blank$ and $blank O A B comma$ respectively, then $fraction numerator a over denominator R subscript 1 end subscript end fraction plus fraction numerator b over denominator R subscript 2 end subscript end fraction plus fraction numerator c over denominator R subscript 3 end subscript end fraction$ has the value equal to

If $´ O ´$ is the circumcentre of $increment A B C blank$ and $blank R subscript 1 end subscript comma R subscript 2 end subscript blank$ and $blank R subscript 3 end subscript$ are the radii of the circumcircles of triangles $O B C comma blank O C A blank$ and $blank O A B comma$ respectively, then $fraction numerator a over denominator R subscript 1 end subscript end fraction plus fraction numerator b over denominator R subscript 2 end subscript end fraction plus fraction numerator c over denominator R subscript 3 end subscript end fraction$ has the value equal to

In a transformer, number of turns in the primary are 140 and that in the secondary are 280. If current in primary is $4 A$ , then that in the secondary is

In a transformer, number of turns in the primary are 140 and that in the secondary are 280. If current in primary is $4 A$ , then that in the secondary is

Physics-General

parallel

A transformer is often filled with oil. The oil used should have

A transformer is often filled with oil. The oil used should have

Physics-General

The figure shows three circuits with identical batteries, inductors and resistances. Rank the circuits according to the currents through the battery just after the switch is closed, greatest first

The figure shows three circuits with identical batteries, inductors and resistances. Rank the circuits according to the currents through the battery just after the switch is closed, greatest first
Physics-General

A square coil of side 25 cm having 1000 turns is rotated with a uniform speed in a magnetic field about an axis perpendicular to the direction of the field. At an instant t, the emf induced in the coil is e =200sin 100 $pi t$ . The magnetic induction is

A square coil of side 25 cm having 1000 turns is rotated with a uniform speed in a magnetic field about an axis perpendicular to the direction of the field. At an instant t, the emf induced in the coil is e =200sin 100 $pi t$ . The magnetic induction is

Physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.