Question

5.085 is the correct answer

Answer 1

Answer: x ≈ 5.085

Explanation:

We will utilize logarithms to help us solve.

Given:

`\displaystyle 4^(x-3)=18`

The logarithm of both sides of the equation:

`\displaystyle log(4^(x-3))=log(18)`

Logarithm power property:

(x - 3)log(4) = log(18)

Divide both sides of the equation by log(4):

x - 3 =
`(log(18))/(log(4))`

Add 3 to both sides of the equation:

x =
`(log(18))/(log(4))` + 3

Compute:

x ≈ 5.085