Question

What is the value of `x` if `2^3(3^(2x + 3)) = 6(2)^2`?

Answer 1

`x = -1`

Explanation:

Isolate the exponent.

`3^(2x + 3) = 24/8`

`3^(2x+ 3) = 3`

We are in common bases--logarithms are not necessary.

`2x + 3 = 1`

`2x = -2`

`x = -1`

Check back in the original equation:

`8(3^(2(-1) + 3)) =^? 24`

`8(3^1) = 24" "color(green)(√)`

Practice Exercises

1. Solve each equation by writing in equivalent bases and using laws of exponents.

a) `3^(2x+ 5) = 9^(x - 2)`

b) `2^(5x + 1)/16^(3x) = 8^(4x + 2)`

Hopefully this helps!