What is 4log_{10}(x-9)-5log_{10}(x) ?

The solution to 4log_{10}(x-9)-5log_{10}(x) is log_{10}(((x-9)^4)/(x^5))

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simplify 4log_{10}(x-9)-5log_{10}(x)

simplify

4 lo g_{10} (x - 9) - 5 lo g_{10} (x)

lo g_{10} (\frac{( x - 9 ) ^{4}}{x ^{5}})

Solution steps

4 lo g_{10} (x - 9) - 5 lo g_{10} (x)

Apply log rule:

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

4 lo g_{10} (x - 9) = lo g_{10} ((x - 9)^{4})

= lo g_{10} ((x - 9)^{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 - 9)^{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 - 9)^{4}) - lo g_{10} (x^{5}) = lo g_{10} (\frac{( x - 9 ) ^{4}}{x ^{5}})

= lo g_{10} (\frac{( x - 9 ) ^{4}}{x ^{5}})

6 lo g_{10} (x) + 7 lo g_{10} (y)

ln (\frac{x ^{2} + y ^{2}}{x + y}) - ln (x + y)

- lo g_{10} (1.5 \cdot 1 0^{- 3})

- ln \frac{x}{2} + 1 + ln \frac{x}{2} - 1

- lo g_{10} (4.7 \cdot 1 0^{- 5})

What is 4log_{10}(x-9)-5log_{10}(x) ?
The solution to 4log_{10}(x-9)-5log_{10}(x) is log_{10}(((x-9)^4)/(x^5))