What is ln(15*e^{t/t}) ?

The solution to ln(15*e^{t/t}) is ln(15)+1

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simplify ln(15*e^{t/t})

simplify

ln (15 \cdot e^{\frac{t}{t}})

ln (15) + 1

Decimal Notation

3.70805 \dots

Solution steps

ln (15 e^{\frac{t}{t}})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (15 e^{\frac{t}{t}}) = ln (15) + ln (e^{\frac{t}{t}})

= ln (15) + ln (e^{\frac{t}{t}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{\frac{t}{t}}) = \frac{t}{t} ln (e)

= ln (15) + \frac{t}{t} ln (e)

Apply rule

\frac{a}{a} = 1

\frac{t}{t} = 1

= ln (15) + 1 \cdot ln (e)

1 \cdot ln (e) = 1

= ln (15) + 1

4.75 + lo g_{10} (\frac{0.15}{0.7})

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