What is log_{5}(x^2-1)-log_{5}(x-1) ?

The solution to log_{5}(x^2-1)-log_{5}(x-1) is log_{5}(x+1)

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simplify log_{5}(x^2-1)-log_{5}(x-1)

simplify

lo g_{5} (x^{2} - 1) - lo g_{5} (x - 1)

lo g_{5} (x + 1)

Solution steps

lo g_{5} (x^{2} - 1) - lo g_{5} (x - 1)

Apply log rule:

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

lo g_{5} (x^{2} - 1) - lo g_{5} (x - 1) = lo g_{5} (\frac{x ^{2} - 1}{x - 1})

= lo g_{5} (\frac{x ^{2} - 1}{x - 1})

Simplify

\frac{x ^{2} - 1}{x - 1} : x + 1

= lo g_{5} (x + 1)

lo g_{10} (10000 x)

- lo g_{10} (1.8 \times 1 0^{- 5})

lo g_{10} (4 x)

3 lo g_{2} (5) + lo g_{2} (3)

lo g_{\frac{1}{4}} (16 z (x^{3} - 27))

What is log_{5}(x^2-1)-log_{5}(x-1) ?
The solution to log_{5}(x^2-1)-log_{5}(x-1) is log_{5}(x+1)