What is 2log_{10}(x)-5log_{10}(x+1) ?

The solution to 2log_{10}(x)-5log_{10}(x+1) is log_{10}((x^2)/((x+1)^5))

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simplify 2log_{10}(x)-5log_{10}(x+1)

simplify

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

lo g_{10} (\frac{x ^{2}}{( x + 1 ) ^{5}})

Solution steps

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

Apply log rule:

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

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

= lo g_{10} (x^{2}) - 5 lo g_{10} (x + 1)

Apply log rule:

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

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

= lo g_{10} (x^{2}) - lo g_{10} ((x + 1)^{5})

Apply log rule:

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

lo g_{10} (x^{2}) - lo g_{10} ((x + 1)^{5}) = lo g_{10} (\frac{x ^{2}}{( x + 1 ) ^{5}})

= lo g_{10} (\frac{x ^{2}}{( x + 1 ) ^{5}})

lo g_{3} (\frac{x ^{4}}{y ^{\frac{3}{5}}})

lo g_{4} (3) + lo g_{4} (10)

\frac{- 4 ln ( 2 ) - 7 ln ( 7 )}{5 ln ( 7 ) - ln ( 2 )}

ln (\frac{A}{B})

lo g_{9} (x) + lo g_{9} (x + 8)

What is 2log_{10}(x)-5log_{10}(x+1) ?
The solution to 2log_{10}(x)-5log_{10}(x+1) is log_{10}((x^2)/((x+1)^5))