simplify ln(3e^x)

Solution

simplify

ln (3 e^{x})

ln (3) + x

Solution steps

ln (3 e^{x})

Apply log rule:

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

ln (3 e^{x}) = ln (3) + ln (e^{x})

= ln (3) + ln (e^{x})

Apply log rule:

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

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

= ln (3) + x ln (e)

x ln (e) = x

= ln (3) + x

ln (\frac{3}{81})

3.15 + lo g_{10} (\frac{1.875}{0.625})

\frac{1}{2} (ln (5) - ln (4))

- 3 ln ∣ x + 2 ∣ + 4 ln ∣ x + 3 ∣

20 lo g_{10} (4 π) - 20 lo g_{10} (300000)