Question

Use the Power Property of Logarithms to write each logarithm as a product of logarithms. Simplify, if possible.

ⓐ ${\log }_7{5}^4$ⓑ $\log x^{100}$

Short answer

ⓐ logarithm expression${\log }_7{5}^4$ as a product of logarithms is${\log }_7{5}^4=4·{\log }_{7}5$

ⓑ logarithm expression$\log x^{100}$ as a product of logarithms is$\log x^{100}=100·\log x$

Step-by-step solution

Step 1. given data  

Given logarithm expressions are

ⓐ${\log }_7{5}^4$

ⓑ$\log x^{100}$

Step 2. part (a)

Use the power Property of the logarithm ${\log }_a\left(m^p\right)=p{\log }_a\left(m\right)$

so${\log }_7{5}^4=4·{\log }_{7}5$

Step 3. part (b)  

Use the power Property of the logarithm ${\log }_a\left(m^p\right)=p{\log }_a\left(m\right)$

so$\log x^{100}=100·\log x$