How do you solve $2 = 16^{x}$ $2= 16^ { x }$ ?

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Answer 1 · 2016-12-03T17:47:59

$x = \frac{1}{4}$ $x=1/4$

$2 = 16^{x}$ $2=16^x$

You need a "common base" on both sides of the equation, in this case a base of 2.

Note that $16 = 2^{4}$ $16=2^4$ and $2 = 2^{1}$ $2=2^1$

$2^{1} = {(2^{4})}^{x}$ $2^1=(2^4)^x$

Use the exponent rule ${(x^{a})}^{b} = x^{a b}$ $(x^a)^b= x^(ab)$

$2^{1} = 2^{4 x}$ $2^1=2^(4x)$

$1 = 4 x a a a$ $1=4xcolor(white)(aaa)$ Set the exponents equal to each other

$\frac{1}{4} = \frac{4 x}{4} a a a$ $1/4=(4x)/4color(white)(aaa)$ Divide both sides by 4

$x = \frac{1}{4}$ $x=1/4$

How do you solve 2=16x2= 16^ { x }?