What is log_{10}((x^2)/((x-5)^2)) ?

The solution to log_{10}((x^2)/((x-5)^2)) is 2log_{10}(x)-2log_{10}(x-5)

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simplify log_{10}((x^2)/((x-5)^2))

simplify

lo g_{10} (\frac{x ^{2}}{( x - 5 ) ^{2}})

2 lo g_{10} (x) - 2 lo g_{10} (x - 5)

Solution steps

lo g_{10} (\frac{x ^{2}}{( x - 5 ) ^{2}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{x ^{2}}{( x - 5 ) ^{2}}) = lo g_{10} (x^{2}) - lo g_{10} ((x - 5)^{2})

= lo g_{10} (x^{2}) - lo g_{10} ((x - 5)^{2})

Apply log rule:

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

lo g_{10} (x^{2}) = 2 lo g_{10} (x)

= 2 lo g_{10} (x) - lo g_{10} ((x - 5)^{2})

Apply log rule:

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

lo g_{10} ((x - 5)^{2}) = 2 lo g_{10} (x - 5)

= 2 lo g_{10} (x) - 2 lo g_{10} (x - 5)

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

\frac{ln ( \frac{41}{16} )}{4 ln ( 2 )}

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5 ln (2) - \frac{1}{2} + 5 ln (3) - 5 ln (1) + 1 - 5 ln (2)

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What is log_{10}((x^2)/((x-5)^2)) ?
The solution to log_{10}((x^2)/((x-5)^2)) is 2log_{10}(x)-2log_{10}(x-5)