Question

if 2^5x/2^x=5√32.then find the value of x.

Answer 1

$\frac{2^{5x} }{2^{x} } = 5\sqrt{32} \\\frac{2^{5x} }{2^{x} } = 5\sqrt{2^{5} } \\\frac{2^{5x} }{2^{x} } = 5. 2^{\frac{1}{5} } \\\frac{2^{5x} }{2^{x} } . \frac{1}{2^{\frac{1}{5} } } = 5\\\frac{2^{5x} }{2^{x+\frac{1}{5} } } = 0\\\frac{5x}{x+\frac{1}{5} } = 0\\\\\\frac{x}{5x+1} =0\\x=0$

Answer 2

The value of x is  $\frac{1}{4}$.

Step-by-step explanation:

Given : If $\frac{ {2}^{5x} }{ {2}^{x} }=\sqrt[5]{32}$

To find : The value of x ?

Solution :

$\frac{ {2}^{5x} }{ {2}^{x} }=\sqrt[5]{32}$

Using exponent rule, $\frac{a^x}{a^y}=a^{x-y}$

${2}^{5x - x} = \sqrt[5]{{2}^{5}}$  

${2}^{4x}={2}^{\frac{5}{5}}$  

${2}^{4x}={2}^{1}$  

Now equating the exponents,

$4x=1$

$x=\frac{1}{4}$

Therefore, the value of x is  .

#Learn more

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