How do you write $3 ln a - 6 ln b$ $3lna - 6lnb$ as a single logarithm?

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Answer 1 · 2015-09-01T16:54:42

$3 ln (a) - 6 ln (b) = ln [\frac{a^{3}}{b^{6}}]$ $3 ln(a) - 6 ln(b) = ln[(a^3)/(b^6)]$

$3 ln (a) - 6 ln (b) \Rightarrow$ $3 ln(a) - 6 ln(b) =>$ use law of logs : $log (m^{n}) = n log (m) :$ $log(m^n) = n log(m):$

$= ln (a^{3}) - ln (b^{6}) \Rightarrow$ $= ln(a^3) - ln(b^6) =>$ use: $log (m) - log (n) = log (\frac{m}{n}) :$ $log(m) - log(n) = log(m/n):$

$= ln [\frac{a^{3}}{b^{6}}]$ $= ln[(a^3)/(b^6)]$

How do you write 3lna−6lnb3lna - 6lnb as a single logarithm?