Question

If $x$ is a positive quantity such that $2^x = 3^{\log_5 2}$, then $x$ is equal to

Accepted Answer

B. Taking $\log_2$ on both sides: $x = \log_2 (3^{\log_5 2}) = (\log_5 2) \cdot \log_2 3 = \frac{\log 2}{\log 5} \cdot \frac{\log 3}{\log 2} = \frac{\log 3}{\log 5} = \log_5 3$. Notice that $1 + \log_5(3/5) = \log_5 5 + \log_5 3 - \log_5 5 = \log_5 3$. So Option B is correct.

Logarithmic Exponential Equation

Explanation

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