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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{1}{3} lo g_{b} (x) + 3 lo g_{b} (y) - 4 lo g_{b} (x)

ln (4) + \frac{1}{3} ln (8)

\frac{1}{2} lo g_{10} (c) + 3 lo g_{10} (d)

- \frac{5}{7} lo g_{2} (\frac{5}{7}) - \frac{2}{7} lo g_{2} (\frac{2}{7})

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

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