Question

Find the value of x so that [( 2/5)^3 ]^2=(2/5)^(2x ).​

Answer 1

Step-by-step explanation:

${ {( \frac{2}{5} }^{3}) }^{2} = { \frac{2}{5} }^{2x} \\ \\ = > { \frac{2}{5} }^{6} = { \frac{2}{5} }^{2x} \\ \\ = > 6 = 2x \\ \\ = > x = \frac{6}{2 } = 3$

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Answer 2

${\mathbf {\blue{S}{\underline{\underline{olution:-}}}}}$

$\mathfrak{\underline{AnswEr:-}}$

• The value of x = 3

$\mathfrak{\underline{Given:-}}$

$\: \: \: \: \: \: \: \sf {\Bigg[ \bigg( \dfrac{2}{5}\bigg)^3 \Bigg]^2 = \bigg(\dfrac{2}{5}\bigg)^{2x} }$

$\mathfrak{\underline{Need\:To\: Find:-}}$

• The value of x = ?

${\mathbf {\blue{E}{\underline{\underline{xplanation:-}}}}}$

$\sf {\Bigg[ \bigg( \dfrac{2}{5}\bigg)^3 \Bigg]^2 = \bigg(\dfrac{2}{5}\bigg)^{2x}}$

$\longrightarrow \sf {\bigg(\dfrac{2}{5}\bigg)^{3 \times 2} = \bigg(\dfrac{2}{5}\bigg)^{2x}}$

$\longrightarrow \sf {\bigg(\dfrac{2}{5}\bigg)^6 = \bigg(\dfrac{2}{5}\bigg)^{2x} }$

Since bases are same, their exponents must be equal.

$\:\:\:\:\dag\bf{\underline \green{ThereFore:-}}$

$\longrightarrow \sf {6x = 2x}$

$\longrightarrow \sf {x = \dfrac{6}{2} }$

$\longrightarrow \sf {x = 3}$

$\:\:\:\:\dag\bf{\underline{\underline \pink{Hence:-}}}$

• The value of x is 3.

$\rule{200}{2}$