Logarithm question

**calvin_coolidge** · August 30th 2008, 10:50 AM

Hello, Need some direction in solving this prob: Solve the following equation for : x 7^x+10=15^10x Write your answer as an expression involving base-10 logarithms Trying to work the rust off of my math skills....Logarithms were never my strong suit. Thanks for any help you might give, ~CC

**o_O** · August 30th 2008, 11:10 AM

$\begin{array}{rcl}{\color{blue}\log (}7^{x+10}{\color{blue})} & = & {\color{blue}\log (}15^{10x}{\color{blue})} \\ (x+10) \cdot \log 7 & = & 10x \cdot \log 15 \quad (\text{Property of logs: } \log a^b = b\log a) \\ (\log 7)x + 10\log 7 & = & (10\log15)x \\ & \vdots & \end{array}$

Should be simple algebra from here.

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