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

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

$x+3=1.4037$

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