Question

power rule independent practice
expand each logarithm.

1. $\log_{9} u^{5}$
2. $\log_{5} u^{4}$
3. $\log_{3} x^{3}$
4. $\log_{3} x^{4}$
5. $\log_{3} 7^{5}$

condense each

Explanation:

Step1: Apply logarithm power rule

The power rule for logarithms states $\log_b(a^n) = n\log_b(a)$.

Step2: Expand each logarithm

1. $\log_{9} u^5 = 5\log_{9} u$
2. $\log_{5} u^4 = 4\log_{5} u$
3. $\log_{3} x^3 = 3\log_{3} x$
4. $\log_{3} x^4 = 4\log_{3} x$
5. $\log_{3} 7^5 = 5\log_{3} 7$

Answer:

1. $5\log_{9} u$
2. $4\log_{5} u$
3. $3\log_{3} x$
4. $4\log_{3} x$
5. $5\log_{3} 7$