Logarithm using the properties

Statement

Express $\log_2 18$ as a function of $a = \log_2 3$.

Solution

One decomposes the argument into factors and applies the product and power properties: $\log_2 18 = \log_2 (2\cdot 3^2) = \log_2 2 + \log_2 3^2 = 1 + 2\log_2 3.$ Since $a = \log_2 3$: $\boxed{\log_2 18 = 1 + 2a}.$

Links

Topics: Logarithmic function
Concepts: Logarithm · Properties of logarithms
Functions: Logarithmic function
Skills: Use formulae
Exercise type: Calculating expressions