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

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

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

simplify

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

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

Solution steps

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

Rewrite as

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

Apply log rule

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

assuming

x \geq 0

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

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