simplify ln(100e^x)

Solution

simplify

ln (100 e^{x})

2 ln (10) + x

Solution steps

ln (100 e^{x})

Apply log rule:

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

ln (100 e^{x}) = ln (100) + ln (e^{x})

= ln (100) + ln (e^{x})

Apply log rule:

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

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

= ln (100) + x ln (e)

x ln (e) = x

= ln (100) + x

ln (100) = 2 ln (10)

= 2 ln (10) + x

- ln (\frac{1}{0.99})

ln (\frac{- 1 \cdot 3 ^{n}}{2 ^{n} b ^{n}})

- \frac{1}{2} ln (7) + \frac{1}{2} ln (5)

\frac{1 3 ^{\frac{2 l n ( 2 )}{l n ( 13 )}} + 10}{6}

ln (\frac{2 n ^{2} + 1}{n ^{2} + 1})