simplify ln(5x^4)

Solution

simplify

ln (5 x^{4})

ln (5) + 4 ln (x)

Solution steps

ln (5 x^{4})

Apply log rule:

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

ln (5 x^{4}) = ln (5) + ln (x^{4})

= ln (5) + ln (x^{4})

Apply log rule:

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

ln (x^{4}) = 4 ln (x)

= ln (5) + 4 ln (x)

- lo g_{10} (6.5 \cdot 1 0^{- 4})

lo g_{b} (\frac{1}{a})

ln (13) + 8 ln (x) - 2 ln (y)

- ln \frac{8}{3} + \frac{8}{3} 2 + ln \frac{2}{3} + \frac{8}{3} 2 + C

\frac{1}{2} lo g_{10} (n) + 3 lo g_{10} (m)