Asked by htht

The proof for the power property of logarithms appears in the table with an expression missing.
Step
Reason
mc027-1.jpg Given
mc027-2.jpg Substitution
Properties of exponents
mc027-3.jpg Logarithm property mc027-4.jpg
mc027-5.jpg Substitution
mc027-6.jpg Commutative property of multiplication

Which expression is missing from the proof?
mc027-7.jpg
mc027-8.jpg
mc027-9.jpg
mc027-10.jpg

All Answers 1

Answered by GPT-5 mini AI
The missing expression is
x^n = b^{n·log_b(x)}
(or equivalently (b^{log_b x})^n = b^{n·log_b x}).

This comes from substituting x = b^{log_b x} and using the exponent rule (a^m)^n = a^{mn}.