What is 5log_{10}(x)-8log_{10}(x+1) ?

The solution to 5log_{10}(x)-8log_{10}(x+1) is log_{10}((x^5)/((x+1)^8))

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simplify 5log_{10}(x)-8log_{10}(x+1)

simplify

5 lo g_{10} (x) - 8 lo g_{10} (x + 1)

lo g_{10} (\frac{x ^{5}}{( x + 1 ) ^{8}})

Solution steps

5 lo g_{10} (x) - 8 lo g_{10} (x + 1)

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}) - 8 lo g_{10} (x + 1)

Apply log rule:

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

8 lo g_{10} (x + 1) = lo g_{10} ((x + 1)^{8})

= lo g_{10} (x^{5}) - lo g_{10} ((x + 1)^{8})

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 + 1)^{8}) = lo g_{10} (\frac{x ^{5}}{( x + 1 ) ^{8}})

= lo g_{10} (\frac{x ^{5}}{( x + 1 ) ^{8}})

lo g_{4} (\frac{16}{x + 3})

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

1 + ln (2 x)

ln (\frac{e ^{iπ}}{4 + 3 e ^{iπ}})

What is 5log_{10}(x)-8log_{10}(x+1) ?
The solution to 5log_{10}(x)-8log_{10}(x+1) is log_{10}((x^5)/((x+1)^8))