What is 3log_{10}(x+1)+log_{10}(y)-2log_{10}(x) ?

The solution to 3log_{10}(x+1)+log_{10}(y)-2log_{10}(x) is log_{10}(((x+1)^3y)/(x^2))

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simplify 3log_{10}(x+1)+log_{10}(y)-2log_{10}(x)

simplify

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

lo g_{10} (\frac{( x + 1 ) ^{3} y}{x ^{2}})

Solution steps

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

Apply log rule:

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

3 lo g_{10} (x + 1) = lo g_{10} ((x + 1)^{3})

= lo g_{10} ((x + 1)^{3}) + lo g_{10} (y) - 2 lo g_{10} (x)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} ((x + 1)^{3}) + lo g_{10} (y) = lo g_{10} (y (x + 1)^{3})

= lo g_{10} ((x + 1)^{3} y) - 2 lo g_{10} (x)

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} (y (x + 1)^{3}) - lo g_{10} (x^{2})

Apply log rule:

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

lo g_{10} (y (x + 1)^{3}) - lo g_{10} (x^{2}) = lo g_{10} (\frac{y ( x + 1 ) ^{3}}{x ^{2}})

= lo g_{10} (\frac{( x + 1 ) ^{3} y}{x ^{2}})

2 lo g_{10} (x) - lo g_{10} (\frac{1}{x}) - lo g_{10} (y)

lo g_{10} (\frac{2 x ^{3} + 4}{5 x ^{3} - x})

33.33 (1) ln (\frac{1100}{1400}) - 0.287 ln (\frac{5}{20})

ln (7) + 2 ln (5)

lo g_{7} (2 x) + lo g_{7} (2) + 5

What is 3log_{10}(x+1)+log_{10}(y)-2log_{10}(x) ?
The solution to 3log_{10}(x+1)+log_{10}(y)-2log_{10}(x) is log_{10}(((x+1)^3y)/(x^2))