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5 If $3 to the power of x plus 1 end exponent equals 9 to the power of x minus 2 end exponent$ , also find the value of $2 to the power of x plus 2 end exponent$ .

hint Hint:

In Mathematics, lets say, "a" represents a number and " n " is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
$a to the power of n equals a cross times a cross times horizontal ellipsis cross times a$ n times.

The correct answer is: 128

Step-by-step solution:-
$3 to the power of x plus 1 end exponent equals 9 to the power of x minus 2 end exponent$
$therefore 3 to the power of left parenthesis x plus 1 right parenthesis end exponent equals 3 to the power of 2 left parenthesis x minus 2 right parenthesis end exponent$
$therefore 3 to the power of left parenthesis x plus 1 right parenthesis end exponent equals 3 to the power of left parenthesis 2 x minus 4 right parenthesis end exponent$ $open square brackets open parentheses b to the power of n close parentheses to the power of m equals b to the power of n m end exponent close square brackets$
$therefore x plus 1 equals 2 x minus 4$ (Exponents of the same base in an equation are equal)
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell therefore 1 plus 4 equals 2 x minus x end cell row cell therefore space of 1em 5 equals straight x end cell row blank end table$
$x equals 5$ $text (Equation i) end text$
$2 to the power of left parenthesis x plus 2 right parenthesis end exponent equals 2 to the power of left parenthesis 5 plus 2 right parenthesis end exponent$ (From Equation i)
$therefore 2 to the power of left parenthesis x plus 2 right parenthesis end exponent equals 2 to the power of 7$
$therefore 2 to the power of left parenthesis x plus 2 right parenthesis end exponent equals 128$

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Are the given triangles congruent? Explain why or why not.

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If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent by

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Find the value of x, y and z

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M ∠ A = (4x + 3)° and m ∠ B = (5x + 6)°
Find the value of x if the angles A and B are
II) Supplementary

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The C.S.A. and T.S.A. of cylinder are in the ratio 1:2. If the T.S.A of the right cylinder is 616 sq. cm, then find its volume?

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M ∠ A = (4x + 3)° and m ∠ B = (5x + 6)°
Find the value of x if the angles A and B are
I) Complementary

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Simplify using the laws of exponents:
$left square bracket 64 divided by 16 right square bracket to the power of negative 3 divided by 4 end exponent cross times open curly brackets left square bracket 25 divided by 8 right square bracket to the power of negative 3 divided by 2 end exponent divided by left square bracket 5 divided by 2 right square bracket to the power of negative 3 end exponent close curly brackets$

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If $vertical line 2 x plus 3 vertical line equals 5$ and $vertical line 3 y minus 3 vertical line equals 6$ , what is one possible value of $vertical line x y vertical line$ ?

Note:
This problem can have different answers if solved differently. Instead of making $2 x plus 3$ positive, if we took $2 x plus 3 less than 0$ , we would get a different answer. Similarly, $3 y minus 3 less than 0$ for , we get a different value of $vertical line x y vertical line$ . If we take both negative, we will get another answer.
Thus, we can get 4 answers: 1,3, 4, 12.

If $vertical line 2 x plus 3 vertical line equals 5$ and $vertical line 3 y minus 3 vertical line equals 6$ , what is one possible value of $vertical line x y vertical line$ ?

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Maths-

In △ ABC, AB = x and BC = x + 1 . How many possible values are there for x if the perimeter of △ ABC is 14?

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5 If , also find the value of .

In Mathematics, lets say, "a" represents a number and " n " is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.n times.

The correct answer is: 128

Step-by-step solution:- (Exponents of the same base in an equation are equal) (From Equation i)

Related Questions to study

What additional information is necessary to prove that the given triangles are congruent by AAS congruence postulate?

What additional information is necessary to prove that the given triangles are congruent by AAS congruence postulate?

Are the given triangles congruent? Explain why or why not.

Are the given triangles congruent? Explain why or why not.

Are the given triangles congruent? Explain why or why not.

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Prove that triangles ACB and ACD are congruent.

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What additional information is necessary to prove that the given triangles are congruent by AAS congruence postulate?

What additional information is necessary to prove that the given triangles are congruent by AAS congruence postulate?

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If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent by

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent by

Find the value of x, y and z

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M ∠ A = (4x + 3)° and m ∠ B = (5x + 6)°Find the value of x if the angles A and B areII) Supplementary

M ∠ A = (4x + 3)° and m ∠ B = (5x + 6)°Find the value of x if the angles A and B areII) Supplementary

The C.S.A. and T.S.A. of cylinder are in the ratio 1:2. If the T.S.A of the right cylinder is 616 sq. cm, then find its volume?

The C.S.A. and T.S.A. of cylinder are in the ratio 1:2. If the T.S.A of the right cylinder is 616 sq. cm, then find its volume?

M ∠ A = (4x + 3)° and m ∠ B = (5x + 6)°Find the value of x if the angles A and B areI) Complementary

M ∠ A = (4x + 3)° and m ∠ B = (5x + 6)°Find the value of x if the angles A and B areI) Complementary

Simplify using the laws of exponents:

Simplify using the laws of exponents:

If and , what is one possible value of ?

If and , what is one possible value of ?

In △ ABC, AB = x and BC = x + 1 . How many possible values are there for x if the perimeter of △ ABC is 14?

In △ ABC, AB = x and BC = x + 1 . How many possible values are there for x if the perimeter of △ ABC is 14?

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5 If $3 to the power of x plus 1 end exponent equals 9 to the power of x minus 2 end exponent$ , also find the value of $2 to the power of x plus 2 end exponent$ .

M ∠ A = (4x + 3)° and m ∠ B = (5x + 6)°
Find the value of x if the angles A and B are
II) Supplementary

M ∠ A = (4x + 3)° and m ∠ B = (5x + 6)°
Find the value of x if the angles A and B are
II) Supplementary

M ∠ A = (4x + 3)° and m ∠ B = (5x + 6)°
Find the value of x if the angles A and B are
I) Complementary

M ∠ A = (4x + 3)° and m ∠ B = (5x + 6)°
Find the value of x if the angles A and B are
I) Complementary

If $vertical line 2 x plus 3 vertical line equals 5$ and $vertical line 3 y minus 3 vertical line equals 6$ , what is one possible value of $vertical line x y vertical line$ ?

If $vertical line 2 x plus 3 vertical line equals 5$ and $vertical line 3 y minus 3 vertical line equals 6$ , what is one possible value of $vertical line x y vertical line$ ?