simplify ln(a^cb^g)

Solution

simplify

ln (a^{c} b^{g})

c ln (a) + g ln (b)

Solution steps

ln (a^{c} b^{g})

Apply log rule:

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

ln (a^{c} b^{g}) = ln (a^{c}) + ln (b^{g})

= ln (a^{c}) + ln (b^{g})

Apply log rule:

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

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

= c ln (a) + ln (b^{g})

Apply log rule:

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

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

= c ln (a) + g ln (b)

- \frac{8.31 \cdot 310}{1 \cdot 9.65 \cdot 1 0 ^{- 4}} \cdot ln (\frac{10}{145})

ln (2) + ln (2) - ln (3)

4 lo g_{10} (2) - 3 lo g_{10} (4) + lo g_{10} (5)

ln (3 x^{2} - 9 x) + ln (\frac{1}{3 x})

- lo g_{10} (3.5 \cdot 1 0^{11})