SOLUTION: solve the logarithmic equation: 9^-r = 9^1-2r -r is a subscript and 1-2r are subscripts and written together I got 1-1r for the answer, but it doesn't seem right

Click here to see ALL problems on Exponential-and-logarithmic-functions

Question 1082041: solve the logarithmic equation: 9^-r = 9^1-2r
-r is a subscript and 1-2r are subscripts and written together
I got 1-1r for the answer, but it doesn't seem right
Found 2 solutions by Theo, solver91311:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
9^(-r) = 9^(1-2r)

this is true if and only if -r = 1 - 2r

add 2r to both sides of the equation to get 2r - r = 1 which becomes r = 1

9^(-r) becomes 9^-1 which becomes 1/9^1 which becomes 1/9

9^(1-2r) becomes 9^(1-2) which becomes 9^-1 which becomes 1/9

the solution of r = 1 is confirmed to be correct.

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Your symbols and your text say two different things.
First you wrote "logarithmic equation" and then you wrote 9^-r = 9^1-2r

The symbols indicate an exponential equation, not logarithmic.

Then you said that -r and 1-2r are subscripts. If that were true then your equation would be

Which makes no sense at all without some additional context.

subscript -- sub, below, like a submarine

superscript -- super, above, like superman

So here is what I think you meant:

Since if and only if we can write:

Solve for

John

My calculator said it, I believe it, that settles it