What is log_{10}((5x-3)^2)+log_{10}((2x+3)^3) ?

The solution to log_{10}((5x-3)^2)+log_{10}((2x+3)^3) is log_{10}((5x-3)^2(2x+3)^3)

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simplify log_{10}((5x-3)^2)+log_{10}((2x+3)^3)

simplify

lo g_{10} ((5 x - 3)^{2}) + lo g_{10} ((2 x + 3)^{3})

lo g_{10} ((5 x - 3)^{2} (2 x + 3)^{3})

Solution steps

lo g_{10} ((5 x - 3)^{2}) + lo g_{10} ((2 x + 3)^{3})

Apply log rule:

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

lo g_{10} ((5 x - 3)^{2}) + lo g_{10} ((2 x + 3)^{3}) = lo g_{10} ((5 x - 3)^{2} (2 x + 3)^{3})

= lo g_{10} ((5 x - 3)^{2} (2 x + 3)^{3})

[3 ln (3) - 1 - 2 ln (2)] - [3 ln (3) - 1 - 2 ln (2)]

ln (24) - ln (3)

ln (\frac{e ^{5}}{10})

lo g_{8} (4 x)

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

What is log_{10}((5x-3)^2)+log_{10}((2x+3)^3) ?
The solution to log_{10}((5x-3)^2)+log_{10}((2x+3)^3) is log_{10}((5x-3)^2(2x+3)^3)