Answer
a. $\ln 175$
b. $\ln \left(\frac{x}{4}\right)$
c. $\ln (5x^3y^{2})$
Work Step by Step
a. Use the Power Property of Logarithms to rewrite the expression:
$\ln7 + \ln 5^{2}$
Use the Product Property of Logarithms to rewrite as a single term:
$=\ln [(7)(5^{2}]$
Evaluate the exponential term first:
$=\ln [7(25)]\\
=\ln 175$
b. Use the Power Property of Logarithms to rewrite the expression:
$\ln x^{3} - \ln (2x)^{2}$
Simplify:
$=\ln x^{3} - \ln (4x^{2})$
Use the Quotient Property of Logarithms to rewrite as a single term:
$=\ln \left(\frac{x^{3}}{4x^{2}}\right)$
Simplify by canceling common terms in the numerator and denominator:
$=\ln \left(\frac{x}{4}\right)$
c. Use the Power Property of Logarithms to rewrite the expression:
$=\ln x^3 + \ln y^{2} + \ln 5$
Use the Product Property of Logarithms to rewrite as a single term:
$=\ln [(x^3)(y^{2})(5)]$
Rewrite in a more conventional way:
$=\ln (5x^3y^{2})$
