What is 5log_{10}(x)-6log_{10}(x-8) ?

The solution to 5log_{10}(x)-6log_{10}(x-8) is log_{10}((x^5)/((x-8)^6))

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simplify 5log_{10}(x)-6log_{10}(x-8)

simplify

5 lo g_{10} (x) - 6 lo g_{10} (x - 8)

lo g_{10} (\frac{x ^{5}}{( x - 8 ) ^{6}})

Solution steps

5 lo g_{10} (x) - 6 lo g_{10} (x - 8)

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^{5}) - 6 lo g_{10} (x - 8)

Apply log rule:

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

6 lo g_{10} (x - 8) = lo g_{10} ((x - 8)^{6})

= lo g_{10} (x^{5}) - lo g_{10} ((x - 8)^{6})

Apply log rule:

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

lo g_{10} (x^{5}) - lo g_{10} ((x - 8)^{6}) = lo g_{10} (\frac{x ^{5}}{( x - 8 ) ^{6}})

= lo g_{10} (\frac{x ^{5}}{( x - 8 ) ^{6}})

ln (x^{2} + 11 x + 30) - ln (x + 6)

- lo g_{e} (2) + 6 lo g_{e} (6) - lo g_{e} (5)

lo g_{2} (x + 3) + 5 lo g_{2} (x - 7) - 3 lo g_{2} (x + 6)

ln (\frac{1.12}{0.031})

ln (2) - ln (9)

What is 5log_{10}(x)-6log_{10}(x-8) ?
The solution to 5log_{10}(x)-6log_{10}(x-8) is log_{10}((x^5)/((x-8)^6))