simplify ln(2e^1)

Solution

simplify

ln (2 e^{1})

ln (2) + 1

Decimal Notation

1.69314 \dots

Solution steps

ln (2 e^{1})

Apply log rule:

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

ln (2 e^{1}) = ln (2) + ln (e^{1})

= ln (2) + ln (e^{1})

Apply log rule:

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

ln (e^{1}) = 1 \cdot ln (e)

= ln (2) + 1 \cdot ln (e)

1 \cdot ln (e) = 1

= ln (2) + 1

lo g_{6} (\frac{w ^{5}}{v})

\frac{1}{2} \cdot ln (3)

lo g_{16} (\frac{9 r}{s})

lo g_{10} (a - b) - lo g_{10} (3)

ln (x^{e} e^{x})