Question

Find 16^(2x+3)/4^(x) =32.

Answer 1

Given :

$\sf \dfrac{ {16}^{(2x + 3)} }{ {4}^{x} } = 32$

To find :

• The value of X

Solution :

$\sf \implies\dfrac{ {16}^{(2x + 3)} }{ {4}^{x} } = 32$

We know that :-

• 2⁴= 16
• 2²=4
• 2⁵= 32

$\sf \implies\dfrac{ { ({2}^{4}) }^{(2x + 3)} }{ { ({2}^{2} )}^{x} } = {2}^{5}$

We know that :-

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

Therefore :-

$\sf \implies\dfrac{ { {2} }^{(8x + 12)} }{ { {2}}^{2x} } = {2}^{5}$

We know that :-

$\sf \dfrac{ {{a}^{n} }}{ {{a}^{m} }} = {a}^{n - m}$

$\sf \implies{ { {2} }^{(8x + 12 - 2x)} } = {2}^{5}$

$\sf \implies{ { {2} }^{(6x + 12 )} } = {2}^{5}$

Therefore now :-

$\sf \implies{6x + 12 } = {5}$

$\sf \implies{6x } = {5} - 12$

$\sf \implies{6x } = -7$

$\sf \implies{x } = \dfrac{ - 7}{6}$

Answer : -7/6