Question

Solve the equation 2^(3x)=8(4^(x-1/2)) for x.

Answer 1

\[8\times 4^{x-\frac{1}{2}}=2^3\times (2^2)^{x-\frac{1}{2}}\]
\[=2^3\times 2^{2x-1}\]
\[=2^{2x-1+3}\]
\[=2^{2x+2}\] is a start

Answer 2

Alright, then what? I don't really understand what to do in any equation if the exponent is a polynomial.

Answer 3

The bases on both sides are the same, so you can equate the powers.
That is 3x = 2x+2 <- solve.

Answer 4

so x=2?