Solve? #16^(3x)=64#

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Answer 1 · 2017-11-14T15:04:40

#x=1/2#

#16^(3x)=64#

Notice that both 16 and 64 can be written as a power of 2:

#16=2^4, 64=2^6#

and so we can write the problem as:

#(2^4)^(3x)=2^6#

We can use the rule #(x^a)^b=x^(ab)# to get on the left hand side:

#2^(12x)=2^6#

We can now equate the powers:

#12x=6#

#x=1/2#