What is 1/3 log_{10}(3x)+2/3 log_{10}(3x) ?

The solution to 1/3 log_{10}(3x)+2/3 log_{10}(3x) is log_{10}(3x)

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simplify 1/3 log_{10}(3x)+2/3 log_{10}(3x)

simplify

\frac{1}{3} lo g_{10} (3 x) + \frac{2}{3} lo g_{10} (3 x)

lo g_{10} (3 x)

Solution steps

\frac{1}{3} lo g_{10} (3 x) + \frac{2}{3} lo g_{10} (3 x)

Factor out common term

lo g_{10} (3 x)

= lo g_{10} (3 x) (\frac{1}{3} + \frac{2}{3})

\frac{1}{3} + \frac{2}{3} = 1

= lo g_{10} (3 x) \cdot 1

Apply rule:

a \cdot 1 = a

= lo g_{10} (3 x)

4 ln (x) + 7 ln (y) - 3 ln (z)

lo g_{10} (\frac{11 x ^{3} y}{z + 1})

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

lo g_{6} (x y)

ln (\frac{4}{9})

What is 1/3 log_{10}(3x)+2/3 log_{10}(3x) ?
The solution to 1/3 log_{10}(3x)+2/3 log_{10}(3x) is log_{10}(3x)