What is the solution to the equation 7 ^(–3x) ≈ 9 ?

Question

anonymous · Answer

$$7^{-3x}\approx9$$

anonymous · Answer

This will have an exact solution. But you can round your answer as well. 

Take the logarithm of both sides and recall the special properties of log

anonymous · Answer

How do you do that?

anonymous · Answer

x = 0.376
x = 0.295
x = –0.376
I ruled out one of the answers, but how do you do it?

anonymous · Answer

$$\log 7^{-3x}=\log9$$

anonymous · Answer

The left hand side can be changed with one of the log properties. Do you know that?

anonymous · Answer

I know that but I don't know how.

anonymous · Answer

http://en.wikipedia.org/wiki/List_of_logarithmic_identities

anonymous · Answer

Here you will use that
$$\log 7^{-3x}=-3xlog7$$

anonymous · Answer

Thus x is
$$x=-\frac{ \log9 }{ 3\log7 }$$

anonymous · Answer

And I just divide that to get -0.376

anonymous · Answer

Maybe, I havent done the calculation. 
Hope that helped, Im going back to watch LOTR

anonymous · Answer

Thank you, enjoy Lord of the Rings! I'll give you a medal.

anonymous · Answer

They are in Moria now :)
YOU SHALL NOT PASS