Answer:
x = 3/4
Step-by-step explanation:
Given 1.5(4)^2x = 12, solve for x.
Divide by 1.5 on each side first.
\(4^{2x} = \frac{12}{1.5}\)
\(4^{2x} = 8\)
We can convert \(4^{2x}\) into a power of 2.
\(4^{2x} = 2^{4x}\)
To solve it, the 8 needs to be in a power of 2 as well.
\(8 = 2^{3}\)
So our equation is now:
\(2^{4x} = 2^3\)
When the bases are the same, the exponents are equal to each other, so we can ignore the bases.
It becomes:
\(4x = 3\)
Solve for x.
\(x = \frac{3}{4}\)
