Question

if 2 power 5 x divided by 2 power x is equal to 5 under root 32 then find the value of x​

Answer 1

The value of x is 1/4.

Step-by-step explanation:

Consider the given equation is

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

We need to find the value of x.

It can be rewritten as

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

Using the properties of exponents we get

$2^{5x-x}=2$               $[\because \dfrac{a^m}{a^n}=a^{m-n}, \sqrt[n]{a^n}=a]$

$2^{4x}=2^1$

On comparing both sides we get

$4x=1$

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

Therefore, the value of x is 1/4.

#Learn more

If 2 ki power 5x divide 2 ki power x is equal to 5 under root 2 ki power 20 then find x.

https://brainly.in/question/10697959

Answer 2

$\frac{2^{5x}}{2^{x}} = \sqrt[5]{32} \: (given)$

$\implies 2^{5x- x } = \sqrt[5]{2^{5}}$

$\boxed { \pink { Since, \frac{a^{m}}{a^{n}} = a^{m-n}}}$

$\implies 2^{4x} = 2^{\frac{5}{5}}$

$\implies 2^{4x} = 2^{1}$

$\implies 4x = 1$

$\boxed { \orange { Since, If \: a^{m} = a^{n} \implies m = n}}$

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

Therefore.,

$\red { Value \:of \: x } \green {=\frac{1}{4} }$

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