How can the logarithm of a number raised to a power be rewritten?
AThe power plus the logarithm
BThe logarithm of the power
CThe power over the logarithm
DThe power times the logarithm
Answer & Solution
Correct answer: D. The power times the logarithm
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_
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