# SOLUTION: I know this shouldn't be hard, we are doing a study sheet for a test and can't get past the second problem. simplify each logarithm (a calculator should not be needed) log ba

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: I know this shouldn't be hard, we are doing a study sheet for a test and can't get past the second problem. simplify each logarithm (a calculator should not be needed) log ba      Log On

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 Question 606063: I know this shouldn't be hard, we are doing a study sheet for a test and can't get past the second problem. simplify each logarithm (a calculator should not be needed) log base (1/3) 9 so this is 1/3^x equals 9 if I use the change of base formula I get -.5 or 1/2 but when I try to work 1/3^(1/2) I don't get 9 what am I doing wrong, and I can't use a calculator anyway so how do I do this without the change of base formula? thank youAnswer by jim_thompson5910(28550)   (Show Source): You can put this solution on YOUR website!Let $\LARGE x = \log_{\frac{1}{3}}\left(9\right)$ Convert this equation to exponential form to get . Now let's solve for x Since the bases are equal (to 3), the exponents must be equal. So or So the solution is Since we let $\LARGE x = \log_{\frac{1}{3}}\left(9\right)$ at the top of the problem, we can say that $\LARGE \text{\color{red}Answer:} \ \color{blue}\boxed{\log_{\frac{1}{3}}\left(9\right) = \color{red} -2}$ Note: you can use the change of base formula to get the same answer of -2. -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------