Question

What is the solution to the equation 7^ -3x ≈ 9 ?

Answer 1

I'm going to assume this is 7^(-3x)=9. First, we take a log base 7 of both sides. That gives us -3x=1.129. We divide both sides by -3 and get x=-.376, our final answer.

Answer 2

I don't think you need to take the base 7 log of both sides... use base e or base 10

so

you get

\[\ln(7^{-3x} ) = \ln (9)\]

applying the log law for powers

you get

\[-3x \times \ln(7) = \ln(9)\]

divide both sides by ln(7)

\[-3x = \frac{\ln(9)}{\ln(7)}\]

then solve for x

the answer above is correct... but use a common log.... not base 7

Answer 3

Yeah, that would make more sense. Common logs are a lot easier to use.