What is log_{10}(a^2b^3) ?

The solution to log_{10}(a^2b^3) is 2log_{10}(a)+3log_{10}(b)

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simplify log_{10}(a^2b^3)

simplify

lo g_{10} (a^{2} b^{3})

2 lo g_{10} (a) + 3 lo g_{10} (b)

Solution steps

lo g_{10} (a^{2} b^{3})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (a^{2} b^{3}) = lo g_{10} (a^{2}) + lo g_{10} (b^{3})

= lo g_{10} (a^{2}) + lo g_{10} (b^{3})

lo g_{10} (a^{2}) = 2 lo g_{10} (a)

lo g_{10} (b^{3}) = 3 lo g_{10} (b)

= 2 lo g_{10} (a) + 3 lo g_{10} (b)

ln (3) - ln (4)

ln (\frac{x}{e ^{3 x}})

7 ln (x) - 3 ln (y)

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

5 ln (2) + 2 ln (3) - 3 ln (4)

What is log_{10}(a^2b^3) ?
The solution to log_{10}(a^2b^3) is 2log_{10}(a)+3log_{10}(b)