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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{b} (b^{3}) = 3 lo g_{b} (b)

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

Apply log rule:

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

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

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

3 lo g_{b} (b) = 3

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

e \cdot ln (\frac{x}{y})

ln (\frac{4 + 12}{2})

ln (\frac{20}{x})

ln ((\frac{m}{8}) (p - 9))

ln (c x^{2})

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