Evaluate: ln(a+b)+5ln(a-b)-4ln(c)

Expression: $\ln\left({a+b}\right)+5\ln\left({a-b}\right)-4\ln\left({c}\right)$

Use $x \times \ln\left({a}\right)=\ln\left({{a}^{x}}\right)$ to transform the expression

$\ln\left({a+b}\right)+\ln\left({{\left( a-b \right)}^{5}}\right)-4\ln\left({c}\right)$

Use $x \times \ln\left({a}\right)=\ln\left({{a}^{x}}\right)$ to transform the expression

$\ln\left({a+b}\right)+\ln\left({{\left( a-b \right)}^{5}}\right)+\ln\left({{c}^{-4}}\right)$

Use the logarithmic product and quotient rules to simplify the expression

$\ln\left({\left( a+b \right) \times {\left( a-b \right)}^{5} \times {c}^{-4}}\right)$

Express with a positive exponent using ${a}^{-n}=\frac{ 1 }{ {a}^{n} }$

$\ln\left({\left( a+b \right) \times {\left( a-b \right)}^{5} \times \frac{ 1 }{ {c}^{4} }}\right)$

Calculate the product

$\ln\left({\frac{ a+b }{ {c}^{4} } \times {\left( a-b \right)}^{5}}\right)$

Calculate the product

$\ln\left({\frac{ \left( a+b \right) \times {\left( a-b \right)}^{5} }{ {c}^{4} }}\right)$

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