Question

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

Answer 1

\[7^{-3x}\approx9\]

Answer 2

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

Answer 3

How do you do that?

Answer 4

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

Answer 5

\[\log 7^{-3x}=\log9\]

Answer 6

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

Answer 7

I know that but I don't know how.

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

And I just divide that to get -0.376

Answer 12

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

Answer 13

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

Answer 14

They are in Moria now :)
YOU SHALL NOT PASS