Question 1

Expand the expression $\log_{25}(25xy)$ as much as possible into a sum or difference of logarithms.

Accepted Answer

$\log_{25}(25) + \log_{25}(x) + \log_{25}(y)$

Question 2

Expand the expression $\log_{4}\left(\frac{7}{x^2}\right)$ as much as possible into a sum or difference of logarithms.

Accepted Answer

$\log_{4}(7) - 2\log_{4}(x)$

Question 3

Expand the expression $\log_{5}\left(\frac{y}{4x}\right)$ as much as possible into a sum or difference of logarithms.

Accepted Answer

$\log_{5}(y) - \log_{5}(4) - \log_{5}(x)$

Question 4

Expand the expression $\log_{10}(100x^2)$ as much as possible into a sum or difference of logarithms.

Accepted Answer

$\log_{10}(100) + \log_{10}(x^2)$

Question 5

Expand the expression $\ln(x^2 \cdot \sqrt{x+3})$ as much as possible into a sum or difference of logarithms.

Accepted Answer

$2\ln(x) + \frac{1}{2}\ln(x+3)$

Expanding Logarithmic Expressions: Sums and Differences

Study Guide - Practice Questions