simplify ln(125e^x)

Solution

simplify

ln (125 e^{x})

3 ln (5) + x

Solution steps

ln (125 e^{x})

Apply log rule:

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

ln (125 e^{x}) = ln (125) + ln (e^{x})

= ln (125) + ln (e^{x})

Apply log rule:

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

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

= ln (125) + x ln (e)

x ln (e) = x

= ln (125) + x

ln (125) = 3 ln (5)

= 3 ln (5) + x

\frac{ln ( 0.17 ) + ln ( 0.19 )}{2}

- lo g_{10} (1.90691 \cdot 1 0^{- 6})

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

ln (\frac{3}{4055})

ln (\frac{x ^{2} x - 4}{4 x + 1})