simplify ln(x*e^r)

Solution

simplify

ln (x \cdot e^{r})

ln (x) + r

Solution steps

ln (x e^{r})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (x) + r ln (e)

r ln (e) = r

= ln (x) + r

2 - 4 \cdot (lo g_{e} (25) - lo g_{e} (13))

ln (x) - ln (v) + ln (v^{2} + 12)

\frac{43 π}{10} + ln (7) - \frac{1}{2} \cdot ln (26) - 169760

ln (\frac{2 x}{e ^{2 x}})

\frac{1}{2} ln (x - 3) + \frac{1}{2} ln (x + 3) - ln (x)