What is ln(4e^{-6/100 t})-ln(0.03t) ?

The solution to ln(4e^{-6/100 t})-ln(0.03t) is ln((133.33333…e^{-(3t)/(50)})/t)

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simplify ln(4e^{-6/100 t})-ln(0.03t)

simplify

ln (4 e^{- \frac{6}{100} t}) - ln (0.03 t)

ln (\frac{133.33333 \dots e ^{- \frac{3 t}{50}}}{t})

Solution steps

ln (4 e^{- \frac{6}{100} t}) - ln (0.03 t)

Apply log rule:

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

ln (4 e^{- \frac{6}{100} t}) - ln (0.03 t) = ln (\frac{4 e ^{- \frac{6}{100} t}}{0.03 t})

= ln (\frac{4 e ^{- \frac{6}{100} t}}{0.03 t})

Simplify

\frac{4 e ^{- \frac{6}{100} t}}{0.03 t} : \frac{133.33333 \dots e ^{- \frac{3 t}{50}}}{t}

= ln (\frac{133.33333 \dots e ^{- \frac{3 t}{50}}}{t})

- lo g_{10} (1.8 \cdot 10)

0.026 ln (5 \cdot 1 0^{12 - 4})

\frac{10 ln ( 8 ) - 10 ln ( 7 )}{8 - 7}

4 ln (3 x + 1) + ln (x - 4)

lo g_{3} (\frac{1}{126})

What is ln(4e^{-6/100 t})-ln(0.03t) ?
The solution to ln(4e^{-6/100 t})-ln(0.03t) is ln((133.33333…e^{-(3t)/(50)})/t)