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

The solution to 3log_{10}(2x)+2log_{10}(x) is log_{10}(8x^5)

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

simplify

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

lo g_{10} (8 x^{5})

Solution steps

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

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

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

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

Apply log rule:

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

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

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

Simplify

(2 x)^{3} x^{2} : 8 x^{5}

= lo g_{10} (8 x^{5})

\frac{1}{2} ln (x) + 2 ln (y) - 3 ln (z)

lo g_{4} (x) - 3 lo g_{4} (y)

lo g_{3} (\frac{g}{27})

lo g_{10} (39284 x^{- 1.799})

What is 3log_{10}(2x)+2log_{10}(x) ?
The solution to 3log_{10}(2x)+2log_{10}(x) is log_{10}(8x^5)