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

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

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

simplify

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

lo g_{a} (x)

Solution steps

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

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

Simplify

\frac{x ^{2}}{( x ) ^{2}} : x

= lo g_{a} (x)

4 lo g_{3} (x^{2} - 1) - 2 lo g_{3} (x + 1)

lo g_{3} (7 \cdot 5)

ln (y e^{- x})

6 lo g_{2} (22) + 1460 - 6 lo g_{2} (24) + 2002

t + ln (t) + ln (v - 2)

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