What is ln((e^{8x}+1)/(e^{-3x)+1}) ?

The solution to ln((e^{8x}+1)/(e^{-3x)+1}) is ln(e^{8x}+1)-ln(e^{-3x}+1)

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simplify ln((e^{8x}+1)/(e^{-3x)+1})

simplify

ln (\frac{e ^{8 x} + 1}{e ^{- 3 x} + 1})

ln (e^{8 x} + 1) - ln (e^{- 3 x} + 1)

Solution steps

ln (\frac{e ^{8 x} + 1}{e ^{- 3 x} + 1})

Apply log rule:

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

ln (\frac{e ^{8 x} + 1}{e ^{- 3 x} + 1}) = ln (e^{8 x} + 1) - ln (e^{- 3 x} + 1)

= ln (e^{8 x} + 1) - ln (e^{- 3 x} + 1)

- \frac{6}{9} lo g_{2} (\frac{6}{9}) - \frac{3}{9} lo g_{2} (\frac{3}{9})

4 lo g_{b} (2) + lo g_{b} (5)

lo g_{7} (2) + lo g_{7} (5)

ln (\frac{8}{5 x ^{5} y})

lo g_{3} (\frac{6 y}{z})

What is ln((e^{8x}+1)/(e^{-3x)+1}) ?
The solution to ln((e^{8x}+1)/(e^{-3x)+1}) is ln(e^{8x}+1)-ln(e^{-3x}+1)