What is ln(60e^{x/3})-ln(e^{x/2}) ?

The solution to ln(60e^{x/3})-ln(e^{x/2}) is ln((60)/(e^{x/6)})

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simplify ln(60e^{x/3})-ln(e^{x/2})

simplify

ln (60 e^{\frac{x}{3}}) - ln (e^{\frac{x}{2}})

ln (\frac{60}{e ^{\frac{x}{6}}})

Solution steps

ln (60 e^{\frac{x}{3}}) - ln (e^{\frac{x}{2}})

Apply log rule:

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

ln (60 e^{\frac{x}{3}}) - ln (e^{\frac{x}{2}}) = ln (\frac{60 e ^{\frac{x}{3}}}{e ^{\frac{x}{2}}})

= ln (\frac{60 e ^{\frac{x}{3}}}{e ^{\frac{x}{2}}})

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{e ^{\frac{x}{3}}}{e ^{\frac{x}{2}}} = e^{\frac{x}{3} - \frac{x}{2}} = e^{- \frac{x}{6}}

= ln (\frac{60}{e ^{\frac{x}{6}}})

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What is ln(60e^{x/3})-ln(e^{x/2}) ?
The solution to ln(60e^{x/3})-ln(e^{x/2}) is ln((60)/(e^{x/6)})