What is log_{b}((a^2b^3)/(c^4m)) ?

The solution to log_{b}((a^2b^3)/(c^4m)) is 2log_{b}(a)+3-4log_{b}(c)-log_{b}(m)

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simplify log_{b}((a^2b^3)/(c^4m))

simplify

lo g_{b} (\frac{a ^{2} b ^{3}}{c ^{4} m})

2 lo g_{b} (a) + 3 - 4 lo g_{b} (c) - lo g_{b} (m)

Solution steps

lo g_{b} (\frac{a ^{2} b ^{3}}{c ^{4} m})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{b} (\frac{a ^{2} b ^{3}}{c ^{4} m}) = lo g_{b} (a^{2} b^{3}) - lo g_{b} (c^{4} m)

= lo g_{b} (a^{2} b^{3}) - lo g_{b} (c^{4} m)

lo g_{b} (a^{2} b^{3}) = 2 lo g_{b} (a) + 3

lo g_{b} (c^{4} m) = 4 lo g_{b} (c) + lo g_{b} (m)

= 2 lo g_{b} (a) + 3 - (4 lo g_{b} (c) + lo g_{b} (m))

Apply the distributive law:

- (a + b) = - a - b

- (4 lo g_{b} (c) + lo g_{b} (m)) = - 4 lo g_{b} (c) - lo g_{b} (m)

= 2 lo g_{b} (a) + 3 - 4 lo g_{b} (c) - lo g_{b} (m)

4 ln (x) + 4 ln (y)

lo g_{8} (2 x^{3})

lo g_{10} (9 x)

lo g_{b} (\frac{4}{c})

lo g_{2} (4 x^{3})

What is log_{b}((a^2b^3)/(c^4m)) ?
The solution to log_{b}((a^2b^3)/(c^4m)) is 2log_{b}(a)+3-4log_{b}(c)-log_{b}(m)