What is ln(800e^{0.05t})-ln(220e^{-0.05t}) ?

The solution to ln(800e^{0.05t})-ln(220e^{-0.05t}) is ln(3.63636…e^{0.1t})

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simplify ln(800e^{0.05t})-ln(220e^{-0.05t})

simplify

ln (800 e^{0.05 t}) - ln (220 e^{- 0.05 t})

ln (3.63636 \dots e^{0.1 t})

Solution steps

ln (800 e^{0.05 t}) - ln (220 e^{- 0.05 t})

Apply log rule:

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

ln (800 e^{0.05 t}) - ln (220 e^{- 0.05 t}) = ln (\frac{800 e ^{0.05 t}}{220 e ^{- 0.05 t}})

= ln (\frac{800 e ^{0.05 t}}{220 e ^{- 0.05 t}})

Simplify

\frac{800 e ^{0.05 t}}{220 e ^{- 0.05 t}} : 3.63636 \dots e^{0.1 t}

= ln (3.63636 \dots e^{0.1 t})

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What is ln(800e^{0.05t})-ln(220e^{-0.05t}) ?
The solution to ln(800e^{0.05t})-ln(220e^{-0.05t}) is ln(3.63636…e^{0.1t})