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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

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

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

Simplify

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

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

ln (x) - 3 [ln (x - 6) + ln (x + 6)]

lo g_{3} (\frac{y}{27})

lo g_{10} (\frac{27}{y})

0.935 - \frac{0.592}{2} lo g_{10} (\frac{0.2}{0. 1 ^{2}})

f (x) = ln (\frac{3 ^{x} 6 ^{3 x}}{2 ^{2 x}})

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