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.
[tex]4^{2x} = \frac{12}{1.5}[/tex]
[tex]4^{2x} = 8[/tex]
We can convert [tex]4^{2x}[/tex] into a power of 2.
[tex]4^{2x} = 2^{4x}[/tex]
To solve it, the 8 needs to be in a power of 2 as well.
[tex]8 = 2^{3}[/tex]
So our equation is now:
[tex]2^{4x} = 2^3[/tex]
When the bases are the same, the exponents are equal to each other, so we can ignore the bases.
It becomes:
[tex]4x = 3[/tex]
Solve for x.
[tex]x = \frac{3}{4}[/tex]
