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

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Answer 1 · 2016-12-03T17:47:59

$x=1/4$

$2=16^x$

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

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

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

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

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

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

$1/4=(4x)/4color(white)(aaa)$ Divide both sides by 4

$x=1/4$

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