Question

If $\log_2(5 + \log_3 a) = 3$ and $\log_5(4a + 12 + \log_2 b) = 3$, then $a + b$ is equal to:

Accepted Answer

B. From first equation: $5 + \log_3 a = 2^3 = 8 \Rightarrow \log_3 a = 3 \Rightarrow a = 3^3 = 27$. Substitute $a = 27$ into second equation: $\log_5(4(27) + 12 + \log_2 b) = 3$ $\log_5(108 + 12 + \log_2 b) = 3 \Rightarrow 120 + \log_2 b = 5^3 = 125$ $\log_2 b = 5 \Rightarrow b = 2^5 = 32$. $a + b = 27 + 32 = 59$.

System of Nested Logarithms

Explanation

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