# Solved Problems of Logarithms

We will use the following formulas to solve the problems of logarithms.

• Product Rule of Logarithm: $\log_a(MN)=\log_a M +\log_a N$

Quotient Rule of Logarithm: $\log_a(M/N)=\log_a M -\log_a N$

Power Rule of Logarithm: $\log_a M^k=k\log_a M$

Base Change Rule of Logarithm: $\log_a M=\log_b M \cdot \log_a b$

Problem 1: Find the value of $\log_3 \log_3 27$

Solution: Note that $27=3^3$

∴ $\log_3 \log_3 27$ $=\log_3 \log_3 3^3$ $=\log_3 3$ $[\because \log_a a^n=n]$

$=1$ $[\because \log_a a=1]$

So $\log_3 \log_3 27=1$

…to be continued.