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

Question

anonymous · Answer

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.

campbell_st · Answer

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

anonymous · Answer

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