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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

Apply log rule:

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

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

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

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

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