Given the exponential equation $4^x = 64$, what is the logarithmic form of the equation in base $10$?
Would it be $\frac{\log_{10}64}{\log_{10}4}$?
$\endgroup$1 Answer
$\begingroup$Starting with $4^x = 64$, take a logarithm on both sides to get
$$\log_{10} 4^x = \log_{10} 64 \implies x \log_{10} 4 = \log_{10} 64 \implies x = \frac{\log_{10} 64}{\log_{10} 4}$$
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