What is expand log_{10}(sqrt((3x)/(4x^2-9))) ?

The solution to expand log_{10}(sqrt((3x)/(4x^2-9))) is 1/2 log_{10}((3x)/(4x^2-9))

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expand log_{10}(sqrt((3x)/(4x^2-9)))

expand

lo g_{10} (\frac{3 x}{4 x ^{2} - 9})

\frac{1}{2} lo g_{10} (\frac{3 x}{4 x ^{2} - 9})

Solution steps

lo g_{10} (\frac{3 x}{4 x ^{2} - 9})

Rewrite as

= lo g_{10} ((\frac{3 x}{4 x ^{2} - 9})^{\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{3 x}{4 x ^{2} - 9})

(sec (x) + tan (x)) cos (x) - sin (x)

\frac{1}{2} + \frac{1}{4} (0.9 - 1)

\frac{n ( n - 1 )}{2}

\frac{24}{( s - 3 ) ^{5}}

\frac{( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

What is expand log_{10}(sqrt((3x)/(4x^2-9))) ?
The solution to expand log_{10}(sqrt((3x)/(4x^2-9))) is 1/2 log_{10}((3x)/(4x^2-9))