Question

2x × 4x = 1 / 8³ × 32^1/5 , find x

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Answer 1

Answer:

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Answer 2

$\huge\color{maroon}\boxed{\colorbox{aqua}{Answer : ♞ }}$

$= > {2}^{x} \times {4}^{x} = {8}^{ \frac{1}{3} } \times {32}^{ \frac{1}{5} }$

$\color {teal}Ignore \: 1 \:in \: the \: powers \: of \: R.H.S$

$\color{tan}so \: we \: get :$

$= > {2}^{x } \times {2}^{2x} = 3\sqrt{8} \times 5\sqrt{32}$

$\color{fuchsia}take \: powers \: commonly \: in \: 2 \: \\ \color{fuchsia}table \: format$

$\color{gold}then :$

$= > {2}^{3x} = 2 \times 2$

$= > {2}^{3x} = 4$

$= > {2}^{3x} = {2}^{2}$

$\color{lime}cancel \: 2 \: on \: lhs \: and \: rhs \: also.$

$= > 3x = 2$

$= > x = \frac{2}{3}$