How would this be simplified? I understand what would be done if the base on the logarithm were 9 but what happens in a case like this? Any help would be greatly appreciated.
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Use the fact that $\displaystyle (x^a)^b=(x^b)^a=x^{ab}$.
Originally Posted by Pernello How would this be simplified? I understand what would be done if the base on the logarithm were 9 but what happens in a case like this? Any help would be greatly appreciated. $\displaystyle \displaystyle \begin{align*} 9^{\log_3{20}} &= \left(3^2\right)^{\log_3{20}} \\ &= 3^{2\log_3{20}} \\ &= 3^{\log_3{\left(20^2\right)}} \\ &= 20^2 \\ &= 400 \end{align*}$
see formula in image, so that u can clear what is the answer 9 log3 20 = 20 log3 9 = 20 log3 (32) = 20 2 log 33 = 20 2 *1 =20 2 = 400
Last edited by skeeter; Jul 26th 2012 at 06:46 AM. Reason: deleted link
x = log(3)20 = log(20) / log(3) ; 9^x = ?
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