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Question

The value of $49 to the power of open parentheses 1 minus log subscript 7 end subscript invisible function application 2 close parentheses end exponent plus 5 to the power of negative log subscript 5 end subscript invisible function application 4 end exponent$ is

$27 / 2$
$25 / 2$
$625 / 16$
None of these

The correct answer is: $25 divided by 2$

$49 to the power of open parentheses 1 minus log subscript 7 end subscript invisible function application 2 close parentheses end exponent plus 5 to the power of negative log subscript 5 end subscript invisible function application 4 end exponent equals 49 cross times 7 to the power of negative 2 log subscript 7 end subscript invisible function application 2 end exponent plus 5 to the power of negative log subscript 5 end subscript invisible function application 4 end exponent equals 49 cross times fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 50 over denominator 4 end fraction equals fraction numerator 25 over denominator 2 end fraction$

Related Questions to study

If $square root of log subscript 2 end subscript invisible function application x end root minus 0.5 equals log subscript 2 end subscript invisible function application square root of x comma$ then $x$ equals

If $square root of log subscript 2 end subscript invisible function application x end root minus 0.5 equals log subscript 2 end subscript invisible function application square root of x comma$ then $x$ equals

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If both the distinct roots of the equation $open vertical bar sin invisible function application x close vertical bar to the power of 2 end exponent plus open vertical bar sin invisible function application x close vertical bar plus b equals 0 blank$ in $blank open square brackets 0 comma pi close square brackets$ are real, then the values of $b$ are

parallel

In triangle $A B C comma$ internal angle bisector $angle A$ makes an angle $theta$ with side $B C.$ The value of $sin invisible function application theta$ is equal to

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If $open parentheses 4 close parentheses to the power of log subscript 9 end subscript invisible function application 3 end exponent plus open parentheses 9 close parentheses to the power of log subscript 2 end subscript invisible function application 4 end exponent equals open parentheses 10 close parentheses to the power of log subscript x end subscript invisible function application 83 end exponent comma$ then $x$ is equal to

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The value of $log invisible function application a b minus log invisible function application open vertical bar b close vertical bar equals$

The value of $log invisible function application a b minus log invisible function application open vertical bar b close vertical bar equals$

parallel

If $alpha comma blank beta comma blank gamma comma blank delta$ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k comma$ then the value of $4 sin invisible function application fraction numerator alpha over denominator 2 end fraction plus 3 sin invisible function application fraction numerator beta over denominator 2 end fraction plus 2 sin invisible function application fraction numerator gamma over denominator 2 end fraction plus sin invisible function application fraction numerator delta over denominator 2 end fraction$ is equal to

If $alpha comma blank beta comma blank gamma comma blank delta$ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k comma$ then the value of $4 sin invisible function application fraction numerator alpha over denominator 2 end fraction plus 3 sin invisible function application fraction numerator beta over denominator 2 end fraction plus 2 sin invisible function application fraction numerator gamma over denominator 2 end fraction plus sin invisible function application fraction numerator delta over denominator 2 end fraction$ is equal to

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parallel

If $log subscript 10 end subscript invisible function application open square brackets fraction numerator 1 over denominator 2 to the power of x end exponent plus blank x minus 1 end fraction close square brackets equals x open square brackets log subscript 10 end subscript invisible function application 5 minus 1 close square brackets comma blank t h e n blank x equals$

If $log subscript 10 end subscript invisible function application open square brackets fraction numerator 1 over denominator 2 to the power of x end exponent plus blank x minus 1 end fraction close square brackets equals x open square brackets log subscript 10 end subscript invisible function application 5 minus 1 close square brackets comma blank t h e n blank x equals$

r triangle $A B C comma blank R equals 5 divided by 2 blank$ and $blank r equals 1.$ Let $I$ be the incentre of the triangle and $D comma blank E$ and $blank F$ be the feet of the perpendiculars from $I blank$ to $blank B C comma blank C A blank$ and $blank A B comma$ respectively. The value of $fraction numerator I D cross times I E cross times I F over denominator I A cross times I B cross times I C end fraction blank$ is equal to

r triangle $A B C comma blank R equals 5 divided by 2 blank$ and $blank r equals 1.$ Let $I$ be the incentre of the triangle and $D comma blank E$ and $blank F$ be the feet of the perpendiculars from $I blank$ to $blank B C comma blank C A blank$ and $blank A B comma$ respectively. The value of $fraction numerator I D cross times I E cross times I F over denominator I A cross times I B cross times I C end fraction blank$ is equal to

any $increment A B C comma$ the value of $a open parentheses b to the power of 2 end exponent plus c to the power of 2 end exponent close parentheses cos invisible function application A plus b left parenthesis c to the power of 2 end exponent plus a to the power of 2 end exponent right parenthesis cos invisible function application B plus c left parenthesis a to the power of 2 end exponent plus b to the power of 2 end exponent right parenthesis cos invisible function application C equals$

any $increment A B C comma$ the value of $a open parentheses b to the power of 2 end exponent plus c to the power of 2 end exponent close parentheses cos invisible function application A plus b left parenthesis c to the power of 2 end exponent plus a to the power of 2 end exponent right parenthesis cos invisible function application B plus c left parenthesis a to the power of 2 end exponent plus b to the power of 2 end exponent right parenthesis cos invisible function application C equals$

parallel

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$tan invisible function application 3 theta plus tan invisible function application theta equals 2 tan invisible function application 2 theta$ , then $blank theta$ is equal to $open parentheses n element of Z close parentheses$

$tan invisible function application 3 theta plus tan invisible function application theta equals 2 tan invisible function application 2 theta$ , then $blank theta$ is equal to $open parentheses n element of Z close parentheses$

e number of solutions of $blank not stretchy sum from r equals 1 to 5 of cos invisible function application r x equals 5$ in the interval $blank open square brackets 0 comma blank 2 pi close square brackets blank$ is

e number of solutions of $blank not stretchy sum from r equals 1 to 5 of cos invisible function application r x equals 5$ in the interval $blank open square brackets 0 comma blank 2 pi close square brackets blank$ is

parallel

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