What is simplify-1/2 log_{10}(s)+3log_{10}(t) ?

The solution to simplify-1/2 log_{10}(s)+3log_{10}(t) is log_{10}((t^3sqrt(s))/s)

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simplify-1/2 log_{10}(s)+3log_{10}(t)

simplify

- \frac{1}{2} lo g_{10} (s) + 3 lo g_{10} (t)

lo g_{10} (\frac{t ^{3} s}{s})

Solution steps

- \frac{1}{2} lo g_{10} (s) + 3 lo g_{10} (t)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} (t^{3}) - lo g_{10} (s^{\frac{1}{2}}) = lo g_{10} (\frac{t ^{3}}{s ^{\frac{1}{2}}})

= lo g_{10} (\frac{t ^{3}}{s ^{\frac{1}{2}}})

Simplify

\frac{t ^{3}}{s ^{\frac{1}{2}}} : \frac{t ^{3} s}{s}

= lo g_{10} (\frac{t ^{3} s}{s})

ln (\frac{x ^{3} - 10}{x ^{3} - 3})

- lo g_{10} (\frac{1}{40000})

ln (\frac{x ^{2}}{5})

\frac{0.125 \cdot 16}{63.617 \cdot 720} \cdot ln (\frac{130}{70})

(75.3) ln (\frac{373}{300})

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