Question

Value of 16 raise to the power log 5 having base 4

Answer 1

Answer:

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Answer 2

$\displaystyle \sf{ {16}^{ log_{4} 5 } = 25 }$

Given :

The expression

$\displaystyle \sf{ {16}^{ log_{4} 5 } }$

To find :

To simplify the expression

Formula :

$\displaystyle \sf{ {a}^{ log_{a} x } = x}$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ {16}^{ log_{4} 5 } }$

Step 2 of 2 :

Simplify the given expression

$\displaystyle \sf{ {16}^{ log_{4} 5 } }$

$\displaystyle \sf{ = {( {4}^{2} )}^{ log_{4} 5 } }$

$\displaystyle \sf{ = {4}^{ 2log_{4} 5 } }$

$\displaystyle \sf{ = {4}^{ log_{4} {5}^{2} } }$

$\displaystyle \sf{ = {4}^{ log_{4} 25 } }$

$\displaystyle \sf{ =25 \: \: (\: \because \: \displaystyle \sf{ {a}^{ log_{a} x } = x } \: \: )}$

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