What is 4log_{10}(x-8)-5log_{10}(x) ?

The solution to 4log_{10}(x-8)-5log_{10}(x) is log_{10}(((x-8)^4)/(x^5))

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simplify 4log_{10}(x-8)-5log_{10}(x)

simplify

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

lo g_{10} (\frac{( x - 8 ) ^{4}}{x ^{5}})

Solution steps

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

Apply log rule:

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

4 lo g_{10} (x - 8) = lo g_{10} ((x - 8)^{4})

= lo g_{10} ((x - 8)^{4}) - 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 - 8)^{4}) - 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 - 8)^{4}) - lo g_{10} (x^{5}) = lo g_{10} (\frac{( x - 8 ) ^{4}}{x ^{5}})

= lo g_{10} (\frac{( x - 8 ) ^{4}}{x ^{5}})

\frac{5}{2} ln (\frac{45}{32})

- lo g_{10} (2.27 \cdot 1 0^{- 7})

- lo g_{10} (5.5 \cdot 1 0^{- 5})

ln (\frac{1}{49 k})

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

What is 4log_{10}(x-8)-5log_{10}(x) ?
The solution to 4log_{10}(x-8)-5log_{10}(x) is log_{10}(((x-8)^4)/(x^5))