Question

if 4^3x-1/16=64 find the value of x
​

Answer 1

The value of x = 2

Correct question : $\displaystyle \sf{ \frac{{4}^{3x - 1}}{16} = 64 }$ find the value of x

Given :

$\displaystyle \sf{ \frac{{4}^{3x - 1}}{16} = 64 }$

To find :

The value of x

Formula :

We are aware of the formula on indices that

$\displaystyle \sf{\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation is

$\displaystyle \sf{ \frac{{4}^{3x - 1}}{16} = 64 }$

Step 2 of 2 :

Find the value of x

$\displaystyle \sf{ \frac{{4}^{3x - 1}}{16} = 64 }$

$\displaystyle \sf{ \implies \frac{{4}^{3x - 1}}{ {4}^{2} } = {4}^{3} }$

$\displaystyle \sf{ \implies {4}^{3x - 1 - 2} = {4}^{3} }\: \: \: \bigg[ \: \because \:\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \bigg]$

$\displaystyle \sf{ \implies {4}^{3x - 3} = {4}^{3} }$

$\displaystyle \sf{ \implies 3x - 3 = 3}$

$\displaystyle \sf{ \implies 3x = 3 + 3}$

$\displaystyle \sf{ \implies 3x = 6}$

$\displaystyle \sf{ \implies x = \frac{6}{3} }$

$\displaystyle \sf{ \implies x = 2 }$

Hence the required value of x = 2

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