What is 6log_{10}(x-2)-5log_{10}(x) ?

The solution to 6log_{10}(x-2)-5log_{10}(x) is log_{10}(((x-2)^6)/(x^5))

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simplify 6log_{10}(x-2)-5log_{10}(x)

simplify

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

lo g_{10} (\frac{( x - 2 ) ^{6}}{x ^{5}})

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

6 lo g_{10} (x - 2) = lo g_{10} ((x - 2)^{6})

= lo g_{10} ((x - 2)^{6}) - 5 lo g_{10} (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{10} ((x - 2)^{6}) - lo g_{10} (x^{5})

Apply log rule:

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

lo g_{10} ((x - 2)^{6}) - lo g_{10} (x^{5}) = lo g_{10} (\frac{( x - 2 ) ^{6}}{x ^{5}})

= lo g_{10} (\frac{( x - 2 ) ^{6}}{x ^{5}})

ln (40) + 2 ln (\frac{1}{2}) + ln (y)

5 ln (6) - 5 ln (2)

ln (\frac{0.025 m ^{3}}{0.016 m ^{3}})

ln (\frac{15}{12})

What is 6log_{10}(x-2)-5log_{10}(x) ?
The solution to 6log_{10}(x-2)-5log_{10}(x) is log_{10}(((x-2)^6)/(x^5))