What is log_{b}((ab^3)/c) ?

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

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simplify log_{b}((ab^3)/c)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{b} (a b^{3}) : lo g_{b} (a) + 3

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

2 ln (a) - ln (2 b) + 2 ln (2)

ln (\frac{27 a}{b})

lo g_{3} (\frac{243 b ^{3} y ^{2} - 4}{y ( x + 4 ) ^{2}})

lo g_{10} (21) - lo g_{10} (3)

lo g_{10} (5 bm)

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