4^x = 64 ⇒ 4^x=4^3 (as 64 is 4^3 ) ⇒ x = 3 (∵ a^m = a^n if and only if m=n for a≠ 0,1, 1) Since x = 3, 2^2x = 64 , and 2x =6 ...

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Comparison of Quantities Using Exponents

If 4x = 64, t...

Question

If $4^{x}$ = 64, then

$2^{2 x} = 64$

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2x = 6

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x = 3

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$10^{x}$ =10000

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Solution

The correct option is C
x = 3

$4^{x} = 64$
$\Rightarrow 4^{x}$ = $4^{3}$ (as 64 is $4^{3}$ )
$\Rightarrow x = 3 (∵ a^{m} = a^{n} i f a n d o n l y i f m = n f o r a \neq 0, 1, - 1)$
Since $x = 3$ , $2^{2 x}$ = 64 , and 2x =6

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