Multiplying logarithms by a constant

When raising a logarithm to a power, you can bring the power out in front as a multiplier:

\log_b(x^k) = k \times \log_b(x)

Splitting up a logarithm with a multiplier

You can also split up a logarithm with a multiplier into a logarithm with an exponent:

k \times \log_b(x) = \log_b(x^k)

Question	Answer
What is the rule for bringing a power out in front of a logarithm?	\log_b(x^k) = k \times \log_b(x)
How do you evaluate \log_2(32^3)?	Bring the power 3 to the front: 3 \times \log_2(32). Since \log_2(32)=5, then 3 \times 5 = 15.
How do you evaluate \log_{10}(1000^4)?	Bring the power 4 to the front: 4 \times \log_{10}(1000). Since \log_{10}(1000)=3, then 4 \times 3 = 12.
How do you rewrite a logarithm with a multiplier (e.g., k \times \log_b(x)) as a single logarithm?	k \times \log_b(x) = \log_b(x^k)
How do you write 4 \times \log_3(9) as a single logarithm?	The power becomes 4: \log_3(9^4) = \log_3(6561).