simplify ln(7*e^x)

Solution

simplify

ln (7 \cdot e^{x})

ln (7) + x

Solution steps

ln (7 e^{x})

Apply log rule:

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

ln (7 e^{x}) = ln (7) + ln (e^{x})

= ln (7) + ln (e^{x})

Apply log rule:

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

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

= ln (7) + x ln (e)

x ln (e) = x

= ln (7) + x

\frac{1}{2} lo g_{10} (b) + 4 lo g_{10} (c)

ln (x + 1) - ln (x)

3 lo g_{5} (3 x + 1) - 2 lo g_{5} (2 x - 1) - lo g_{5} (x)

ln (x) + ln (18)

ln (a + b) + ln (a - b) - 4 ln (c)