Question

if 64 power x = 2√2 then x is​

Answer 1

Answer:

$64 {}^{x} = 2 \sqrt{2} \\ = 64 {}^{x} = 2 \times 2 {}^{ \frac{1}{2} } \\ = 2 {}^{6x} = 2 {}^{ \frac{3}{2} } \\ = 6x = \frac{3}{2} \\ = x = \frac{3}{12}$

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Answer 2

${\huge{\boxed {\rm{\purple {Q}}{\orange{U}}{\red{E}}{\green{S}}{\pink{T}}{\blue{I}}{\red{o}}{\green{n}}}}}$

$if 64^x = 2\sqrt{2} then \: find \: x$

${\huge{\boxed {\rm{\purple {A}}{\orange{N}}{\red{S}}{\green{W}}{\pink{E}}{\blue{R}}}}}$

$\sf\implies 64 ^x = 2\sqrt{2}$

$\sf\implies 2^{6x} = 2\times 2 ^{\frac{1}{2}}$

• $x^a\times x^b = x ^{a+b}$

$\sf\implies 2^{6x} = 2 ^{1 + \frac{1}{2}}$

• if the bases are equal then power will also be equal and vice versa

$\sf\implies 6x = 1 + \dfrac{1}{2}$

$\sf\implies 6x = \dfrac{2+1}{2}$

$\sf\implies 6x = \dfrac{3}{2}$

$\sf\implies x = \dfrac{\cancel 3}{2\times\cancel 6}$

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

${\bold{\blue{\boxed{\bf{x = \dfrac{1}{2}}}}}}$