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.

Question

asked Oct 25, 2021 173k views

1 Answer

Mdakin · Answer 1 · 2021-10-31T16:16:14+0000

Answer:

x=-1.596

Explanation:

We want to solve the equation

4^((x + 3)) = 7

for
.

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

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