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#