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Artemon [7]
3 years ago
14

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

o the nearest thousandth.
Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
6 0

Answer:

x=-1.596

Step-by-step 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)=\frac{log_d(n)}{log_d(b)}

For log_4(7) this gives:

log_4(7)=\frac{log_{10}(7)}{log_{10}(4)}=1.4037

Thus we have

x+3=1.4037

\boxed{\therefore x=-1.596.}

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