simplify ln(2m^8)

Solution

simplify

ln (2 m^{8})

ln (2) + 8 ln (m)

Solution steps

ln (2 m^{8})

Apply log rule:

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

ln (2 m^{8}) = ln (2) + ln (m^{8})

= ln (2) + ln (m^{8})

Apply log rule:

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

ln (m^{8}) = 8 ln (m)

= ln (2) + 8 ln (m)

lo g_{10} (\frac{x}{y ^{3} z ^{2}})

lo g_{10} (\frac{x ^{17} y ^{2}}{z ^{16}})

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

2 lo g_{a} (x^{4}) + 4 lo g_{a} ((2 x)^{2})

4 ln (x) - \frac{1}{7} ln (y)