Question

If 2^5^x÷2^x=5√32.then find the value of x​

Answer 1

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$\Huge{\red{\underline{\textsf{Answer}}}}$

$\large{\green{\underline{\tt{Given:-}}}}$ $\sf \frac{2^{5x}}{2^x}\: = \: \sqrt[5]{32}$

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$\large{\orange{\underline{\tt{To\:find:-}}}}$ $\sf The\: value \:of \:x$

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$\large{\red{\underline{\tt{Solution:-}}}}$

$\longrightarrow$ $\sf 2^{5x-x}\: = \: \sqrt[5]{2^{5}}$

$\longrightarrow$ $\sf 2^{4x}\: = \: 2^{\frac{5}{5}}$

$\longrightarrow$ $\sf 4x\: = \:1$ ( By equating the exponents)

$\pink\longrightarrow$ $\boxed{\pink{\sf \frac{1}{4}}}$ $\orange\star$

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Answer 2

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$\huge\tt{\underline{Solution:}}$

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

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

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

$4x = 1$

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

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