How can the logarithm of a number raised to a power be rewritten?

1. The logarithmic laws are built directly on the exponential laws. 2. Raising a number to a power repeats a multiplication, and logarithms turn multiplication into addition. 3. Repeated addition of the same logarithm is the same as multiplying that logarithm by the power. 4. So the logarithm of a number raised to a power is the power multiplied by the logarithm of the number. 5. Adding the power instead would mix a plain number in with a logarithm, which is not a valid step. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 2: Functions_