What is log_{a}(3x^2)-2log_{a}(x) ?

The solution to log_{a}(3x^2)-2log_{a}(x) is log_{a}(3)

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simplify log_{a}(3x^2)-2log_{a}(x)

simplify

lo g_{a} (3 x^{2}) - 2 lo g_{a} (x)

lo g_{a} (3)

Solution steps

lo g_{a} (3 x^{2}) - 2 lo g_{a} (x)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

- 2 lo g_{a} (x) = - lo g_{a} (x^{2})

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{a} (3 x^{2}) - lo g_{a} (x^{2}) = lo g_{a} (\frac{3 x ^{2}}{x ^{2}})

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

Simplify

\frac{3 x ^{2}}{x ^{2}} : 3

= lo g_{a} (3)

lo g_{a} (5) + lo g_{a} (4)

ln (\frac{4}{k})

0.02 ln (\frac{8}{3})

\frac{3}{2} lo g_{4} (5 t^{6}) - \frac{3}{4} lo g_{4} (t^{4})

- 9 lo g_{10} (y) + 7 lo g_{10} (x)

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