Use the properties of logarithms to expand the logarithmic expression. Wherever possible, evaluate logarithmic expressions.
\[
\ln \left(\frac{a^{3} b^{4}}{c^{2}}\right)
\]
$\ln \left(\frac{a^{3} b^{4}}{c^{2}}\right)=\square$ (Type an exact answer in simplified form.)
Answer
\( \boxed{\ln(a^{3}) + \ln(b^{4}) - \ln(c^{2})} \)
Step 1 ：Use the properties of logarithms to expand the logarithmic expression
Step 2 ：Apply the quotient rule: the logarithm of a quotient is equal to the difference of the logarithms of the numerator and the denominator
Step 3 ：Apply the power rule: the logarithm of a number raised to a power is equal to the power times the logarithm of the number
Step 4 ：Expand the expression: \( \ln \left(\frac{a^{3} b^{4}}{c^{2}}\right) = \ln(a^{3}) + \ln(b^{4}) - \ln(c^{2}) \)
Step 5 ：\( \boxed{\ln(a^{3}) + \ln(b^{4}) - \ln(c^{2})} \)
