simplify ln(2e^6)

Solution

simplify

ln (2 e^{6})

ln (2) + 6

Decimal Notation

6.69314 \dots

Solution steps

ln (2 e^{6})

Apply log rule:

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

ln (2 e^{6}) = ln (2) + ln (e^{6})

= ln (2) + ln (e^{6})

Apply log rule:

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

ln (e^{6}) = 6 ln (e)

= ln (2) + 6 ln (e)

6 ln (e) = 6

= ln (2) + 6

ln (\frac{1 + 5}{2})

lo g_{4} (\frac{c ^{\frac{1}{8}}}{c ^{8}})

2 lo g_{10} (x) + 3 lo g_{10} (x y)

ln (2 e^{4})

ln (\frac{e}{11})