What is log_{5}(x^2)-3log_{5}(x) ?

The solution to log_{5}(x^2)-3log_{5}(x) is -log_{5}(x)

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simplify log_{5}(x^2)-3log_{5}(x)

simplify

lo g_{5} (x^{2}) - 3 lo g_{5} (x)

- lo g_{5} (x)

Solution steps

lo g_{5} (x^{2}) - 3 lo g_{5} (x)

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{5} (x^{2}) = 2 lo g_{5} (x)

= 2 lo g_{5} (x) - 3 lo g_{5} (x)

Add similar elements:

2 lo g_{5} (x) - 3 lo g_{5} (x) = - lo g_{5} (x)

= - lo g_{5} (x)

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

y (ln (x) - ln (y))

3 lo g_{9} (2) - 2 lo g_{9} (5)

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

ln (\frac{5}{7})

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