Question

Explain how solve 4^(x + 3) = 7 using the change of base formula. Include the solution for x in your answer. Round your answer to the nearest thousandth.

Answer 1

`x=-1.596`

Explanation:

We want to solve the equation

`4^((x + 3)) = 7`

for
`x`.

To do that we take the
`log_4` of both sides:

`log_4(4^((x + 3))) = log_4(7)`

`=x+3=log_4(7)`

For the logarithm on the right side we use the change-of-base formula which says:

`log_b(n)=(log_d(n))/(log_d(b))`

For
`log_4(7)` this gives:

`log_4(7)=(log_(10)(7))/(log_(10)(4))=1.4037`

Thus we have

`x+3=1.4037`

`\boxed{\therefore x=-1.596.}`