The solution of the equation can be expressed in the form . What is ?
Pick one
Solution
This problem is quickly solved with knowledge of the laws of exponents and logarithms.
\begin{align*} 7^{x+7} &= 8^x \\ 7^x*7^7 &= 8^x \\ \left(\frac{8}{7}\right)^x &= 7^7 \\ x &= \log_{8/7}7^7 \end{align*}
Since we are looking for the base of the logarithm, our answer is .
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