Your solution is correct.
Yes, exponentiation is a one-to-one function: if a > 1 or 0 < a < 1, then a^x = a^y implies x = y for all x and y.I assumed that since both have the same bases, I can equate x to 2.
Hey guys, for the following question how do I solve for x?
(2^3)^x = 2^6
I know that to raise a power to a power I need to multiply the exponents. In the above question I thought that maybe I can solve it by dividing the exponents, but my math book doesn't mention anything about dividing exponents.
here's how I tried to solve it:
(2^3)^x = 2^6
(2^3)^x = (2^3)^2
x = 2
I assumed that since both have the same bases, I can equate x to 2.