What is log_{10}(x)-1/2 log_{10}(x^2+8) ?

The solution to log_{10}(x)-1/2 log_{10}(x^2+8) is log_{10}((xsqrt(x^2+8))/(x^2+8))

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simplify log_{10}(x)-1/2 log_{10}(x^2+8)

simplify

lo g_{10} (x) - \frac{1}{2} lo g_{10} (x^{2} + 8)

lo g_{10} (\frac{x x ^{2} + 8}{x ^{2} + 8})

Solution steps

lo g_{10} (x) - \frac{1}{2} lo g_{10} (x^{2} + 8)

Apply log rule:

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

\frac{1}{2} lo g_{10} (x^{2} + 8) = lo g_{10} ((x^{2} + 8)^{\frac{1}{2}})

= lo g_{10} (x) - lo g_{10} ((x^{2} + 8)^{\frac{1}{2}})

Apply log rule:

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

lo g_{10} (x) - lo g_{10} ((x^{2} + 8)^{\frac{1}{2}}) = lo g_{10} (\frac{x}{( x ^{2} + 8 ) ^{\frac{1}{2}}})

= lo g_{10} (\frac{x}{( x ^{2} + 8 ) ^{\frac{1}{2}}})

Simplify

\frac{x}{( x ^{2} + 8 ) ^{\frac{1}{2}}} : \frac{x x ^{2} + 8}{x ^{2} + 8}

= lo g_{10} (\frac{x x ^{2} + 8}{x ^{2} + 8})

ln (\frac{5}{15})

ln (\frac{0.0141300000000 \dots}{v ^{1.8}})

ln (e^{3 x} (1 - 2 x)^{- 2})

ln (x) + v + ln (v - 1)

3 lo g_{10} (X) + 2 lo g_{z} (5) - lo g_{10} (y)

What is log_{10}(x)-1/2 log_{10}(x^2+8) ?
The solution to log_{10}(x)-1/2 log_{10}(x^2+8) is log_{10}((xsqrt(x^2+8))/(x^2+8))