Use the properties of logarithms to expand the logarithmic expression. Wherever possible, evaluate logarithmic expressions.
$\ln (\frac{a^{3} b^{4}}{c^{2}})$
$\ln (\frac{a^{3} b^{4}}{c^{2}}) = ◻$ (Type an exact answer in simplified form.)

Answer

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Answer

$\ln (a^{3}) + \ln (b^{4}) - \ln (c^{2})$

Steps

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: $\ln (\frac{a^{3} b^{4}}{c^{2}}) = \ln (a^{3}) + \ln (b^{4}) - \ln (c^{2})$

Step 5 ： $\ln (a^{3}) + \ln (b^{4}) - \ln (c^{2})$