What is log_{10}(4x)+2log_{10}(x-3) ?

The solution to log_{10}(4x)+2log_{10}(x-3) is log_{10}(4x(x-3)^2)

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simplify log_{10}(4x)+2log_{10}(x-3)

simplify

lo g_{10} (4 x) + 2 lo g_{10} (x - 3)

lo g_{10} (4 x (x - 3)^{2})

Solution steps

lo g_{10} (4 x) + 2 lo g_{10} (x - 3)

Apply log rule:

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

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

= lo g_{10} (4 x) + lo g_{10} ((x - 3)^{2})

Apply log rule:

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

lo g_{10} (4 x) + lo g_{10} ((x - 3)^{2}) = lo g_{10} (4 x (x - 3)^{2})

= lo g_{10} (4 x (x - 3)^{2})

7 ln (x) - \frac{1}{4} ln (y)

lo g_{8} (64 x^{2})

5 lo g_{2} (5) + 5 lo g_{2} (7) - 15 lo g_{2} (6)

ln (\frac{1 + 2 x}{1 - x})

lo g_{b} (x^{2} y^{3})

What is log_{10}(4x)+2log_{10}(x-3) ?
The solution to log_{10}(4x)+2log_{10}(x-3) is log_{10}(4x(x-3)^2)