Question

What is the x in 16 raise to power 3x =32 raise to power 5x-13

Answer 1

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Answer 2

SOLUTION

TO DETERMINE

The value of x when

$\sf{ {(16)}^{3x} = {(32)}^{5x - 13} }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that

$\sf{ {( {a}^{m} )}^{n} = {a}^{mn} }$

EVALUATION

$\sf{ {(16)}^{3x} = {(32)}^{5x - 13} }$

$\implies \sf{ {( {2}^{4}) }^{3x} = { ({2}^{5} )}^{5x - 13} }$

$\sf{ \implies {2 }^{12x} = {2}^{(25x - 65)} } \: \: by \: above \: formula$

$\sf{ \implies 12x = 25x - 65}$

$\sf{ \implies 12x - 25x = - 65}$

$\sf{ \implies - 13x = - 65}$

$\sf{ \implies x = 5}$

FINAL ANSWER

The required value x = 5

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