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

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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(3296) (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 can be rewritten as . Using this on your equation, , we get:

(since log (without a base) is a base 10 log).
We can now solve this. Start by simplifying the left side:

Now we can multiply both sides by 1/9 (or divide by 9):