SOLUTION: Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this. log9x = -3 I'm not even sure which equation to use with this. O

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this. log9x = -3 I'm not even sure which equation to use with this. O      Log On


   

Question 212862: Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this.
log9x = -3
I'm not even sure which equation to use with this. Or how I need to put it together? Would it be something like x=log9-3? If not can someone please show me how to I should start and complete this problem.

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Solving an equation for x means getting x by itself on one side of the equation. In your equation the x in in the argument of a log function. Somehow we need to be able to extract the x from the argument of log. The simplest, most common way to do this is to rewrite the equation in exponential form. In general log%28a%2C+b%29+=+c can be rewritten as a%5Ec+=+b. Using this on your equation, log%28%289x%29%29+=+-3, we get:
10%5E%28-3%29+=+9x
(since log (without a base) is a base 10 log).
We can now solve this. Start by simplifying the left side:
1%2F%2810%5E3%29+=+9x
1%2F1000+=+9x
Now we can multiply both sides by 1/9 (or divide by 9):
%281%2F9%29%281%2F1000%29+=+%281%2F9%299x
1%2F9000+=+x