How do you solve #2^(6x) = 16^3#?

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Answer 1 · 2018-03-05T21:00:29

#x=2#

When you are working with an exponential equation where the variable is in the index, it helps to know the powers of the numbers up to #10#

#16# is a power of #2" "rarr 16 =2^4#,

You can write both sides of the equation with the same base.

#2^(6x) = 16^3#

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

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

If the bases are equal, the indices must be equal:

#:. 6x=12#

#x=2#

Answer 2 · 2018-03-05T21:02:35

Given: #2^(6x) = 16^3#

We know that #16 = 2^4#

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

We know that #(b^a)^c = b^(ac)#

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

Matching exponents:

#6x = 12#

#x = 2#