Concept preview

What you will be able to do

1. 01Expand and condense logarithmic expressions with the product, quotient, and power laws
2. 02Use change of base to evaluate any logarithm
3. 03Solve logarithmic and exponential equations, checking for extraneous roots

Because logarithms are exponents, they inherit the exponent rules. The product law turns a product into a sum: $\log_b(MN) = \log_b M + \log_b N$. The quotient law turns a quotient into a difference: $\log_b\!\left(\dfrac{M}{N}\right) = \log_b M - \log_b N$. The power law pulls an exponent out front: $\log_b(M^{p}) = p\log_b M$. These three convert multiplication into addition — the reason logarithms once powered slide rules and hand computation.