5 Use properties of logarithms to condense the logarithmic e

5. Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. Show your work.

1/3[3ln (x+3) - ln x - ln (x² - 3)]

Solution

We have given 1/3[3ln (x+3) - ln x - ln (x² - 3)]

=1/3[ln(x+3)³ - ln x - ln (x² - 3)]

=1/3[ln((x+3)³/x)- ln (x² - 3)] since ln(x)-ln(y)=ln(x/y) and n*n(x)=lnxⁿ

=1/3[ln(((x+3)³/x)/(x² - 3))]

=1/3[ln((x+3)³/(x*(x² - 3)))]

=ln((x+3)³/(x*(x² - 3)))^1/3

1/3[3ln (x+3) - ln x - ln (x² - 3)] =ln((x+3)³/(x*(x² - 3)))^1/3