What is expand log_{10}(sqrt((x-1)/(x^2-4))) ?

The solution to expand log_{10}(sqrt((x-1)/(x^2-4))) is 1/2 log_{10}((x-1)/(x^2-4))

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expand log_{10}(sqrt((x-1)/(x^2-4)))

expand

lo g_{10} (\frac{x - 1}{x ^{2} - 4})

\frac{1}{2} lo g_{10} (\frac{x - 1}{x ^{2} - 4})

Solution steps

lo g_{10} (\frac{x - 1}{x ^{2} - 4})

Rewrite as

= lo g_{10} ((\frac{x - 1}{x ^{2} - 4})^{\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_{10} (\frac{x - 1}{x ^{2} - 4})

x (0 = 2 - \frac{15}{2 x})

- \frac{a s}{( a ^{2} - s ^{2} ) ( a ^{2} + s ^{2} )}

(\frac{1}{2 x ^{2}} - x^{3})^{10}

\frac{x ( x + 1 )}{( x - 1 )}

(2 x + 8 y) (9 x + 2 y)

What is expand log_{10}(sqrt((x-1)/(x^2-4))) ?
The solution to expand log_{10}(sqrt((x-1)/(x^2-4))) is 1/2 log_{10}((x-1)/(x^2-4))