simplify ln(a^5b^4)

Solution

simplify

ln (a^{5} b^{4})

5 ln (a) + 4 ln (b)

Solution steps

ln (a^{5} b^{4})

Apply log rule:

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

ln (a^{5} b^{4}) = ln (a^{5}) + ln (b^{4})

= ln (a^{5}) + ln (b^{4})

Apply log rule:

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

ln (a^{5}) = 5 ln (a)

= 5 ln (a) + ln (b^{4})

Apply log rule:

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

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

= 5 ln (a) + 4 ln (b)

- ln ∣ x - 1 ∣ + ln ∣ x - 2 ∣

3.37 + lo g_{10} (\frac{0.1}{0.9})

ln (0.12 x) + 4 - (0.6 x - 0.7)^{3}

ln (\frac{0.001}{0.1})

\frac{1}{8} ln (3)