What is ln(6)e^3-ln(2)e^{-5} ?

The solution to ln(6)e^3-ln(2)e^{-5} is ln(2^{(e^8-1)/(e^5)}*3^{e^3})

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simplify ln(6)e^3-ln(2)e^{-5}

simplify

ln (6) e^{3} - ln (2) e^{- 5}

ln (2^{\frac{e ^{8} - 1}{e ^{5}}} \cdot 3^{e^{3}})

Solution steps

ln (6) e^{3} - ln (2) e^{- 5}

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

e^{3} ln (6) = ln (6^{e^{3}})

= ln (6^{e^{3}}) - e^{- 5} ln (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

e^{- 5} ln (2) = ln (2^{e^{- 5}})

= ln (6^{e^{3}}) - ln (2^{e^{- 5}})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (6^{e^{3}}) - ln (2^{e^{- 5}}) = ln (\frac{6 ^{e^{3}}}{2 ^{e^{- 5}}})

= ln (\frac{6 ^{e^{3}}}{2 ^{e^{- 5}}})

\frac{6 ^{e^{3}}}{2 ^{e^{- 5}}} = 2^{\frac{e ^{8} - 1}{e ^{5}}} \cdot 3^{e^{3}}

= ln (2^{\frac{e ^{8} - 1}{e ^{5}}} \cdot 3^{e^{3}})

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ln (\frac{1.111}{0.1296})

What is ln(6)e^3-ln(2)e^{-5} ?
The solution to ln(6)e^3-ln(2)e^{-5} is ln(2^{(e^8-1)/(e^5)}*3^{e^3})