What is 2+3log_{10}(x)-1/2 log_{10}(x+7) ?

The solution to 2+3log_{10}(x)-1/2 log_{10}(x+7) is 2+log_{10}((x^3sqrt(x+7))/(x+7))

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simplify 2+3log_{10}(x)-1/2 log_{10}(x+7)

simplify

2 + 3 lo g_{10} (x) - \frac{1}{2} lo g_{10} (x + 7)

2 + lo g_{10} (\frac{x ^{3} x + 7}{x + 7})

Solution steps

2 + 3 lo g_{10} (x) - \frac{1}{2} lo g_{10} (x + 7)

Apply log rule:

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

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

= 2 + lo g_{10} (x^{3}) - \frac{1}{2} lo g_{10} (x + 7)

Apply log rule:

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

\frac{1}{2} lo g_{10} (x + 7) = lo g_{10} ((x + 7)^{\frac{1}{2}})

= 2 + lo g_{10} (x^{3}) - lo g_{10} ((x + 7)^{\frac{1}{2}})

Apply log rule:

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

lo g_{10} (x^{3}) - lo g_{10} ((x + 7)^{\frac{1}{2}}) = lo g_{10} (\frac{x ^{3}}{( x + 7 ) ^{\frac{1}{2}}})

= 2 + lo g_{10} (\frac{x ^{3}}{( x + 7 ) ^{\frac{1}{2}}})

Simplify

\frac{x ^{3}}{( x + 7 ) ^{\frac{1}{2}}} : \frac{x ^{3} x + 7}{x + 7}

= 2 + lo g_{10} (\frac{x ^{3} x + 7}{x + 7})

lo g_{a} (\frac{y ^{5} w ^{2}}{x ^{4} z ^{3}})

ln (\frac{1}{( r - 1 ) !} θ^{- r} x^{(r - 1)} e^{(- x θ - 1)})

ln (4) + 4 ln (3)

2400 + \frac{1}{7.13 \cdot 1 0 ^{- 4}} \cdot ln (\frac{1}{0.9})

- ln (x) + 2 ln (x + 1)

What is 2+3log_{10}(x)-1/2 log_{10}(x+7) ?
The solution to 2+3log_{10}(x)-1/2 log_{10}(x+7) is 2+log_{10}((x^3sqrt(x+7))/(x+7))