What is 1/2 log_{10}(s)+3log_{10}(m) ?

The solution to 1/2 log_{10}(s)+3log_{10}(m) is log_{10}(s^{1/2}m^3)

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

simplify

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

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

Solution steps

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

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} (m)

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

- lo g_{10} (7.46 \cdot 1 0^{- 6})

ln (5) + ln (6)

ln (x + 3) + ln (x - 3)

ln (5) + ln (4)

e^{- \frac{2}{3} (2 l n ∣ 2 x^{3} - 1 ∣ - l n ∣ x^{3} ∣) + C}

What is 1/2 log_{10}(s)+3log_{10}(m) ?
The solution to 1/2 log_{10}(s)+3log_{10}(m) is log_{10}(s^{1/2}m^3)