Question

$if {2}^{5x} \div {2}^{x} = \sqrt[5]{32} find \: the \: value \: of \: x$
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Answer 1

Step-by-step explanation:

${\red{\underline{\underline{\bold{Given:-}}}}}$

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

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The value of x

${\green{\underline{\underline{\bold{Solution:-}}}}}$

$\frac{ {2}^{5x} }{ {2}^{x} } = \sqrt[5]{32} \: \: \: \: ( \therefore \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} ) \\ \\ \implies {2}^{5x - x} = \sqrt[5]{32} \\ \\ 32 \: can \: be \: written \: as \: 2 \times 2 \times 2 \times 2 \times 2 = {2}^{5} \\ \\ \implies {2}^{4x} = \sqrt[5]{ {2}^{5} } \\ \\ \implies {2}^{4x} = { ({2}^{5} )}^{ \frac{1}{5} } \: \: \: \: ( \therefore \: if \: \sqrt[n]{a} = {a}^{ \frac{1}{n} }) \\ \\ \implies {2}^{4x} = 2 \\ \\ \implies 4x = 1 \: \: \: \: ( \therefore \: if \: {a}^{m} = {a}^{n} \: then \: m = n)$

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