What is log_{10}(K)+3log_{10}(L)-5log_{10}(T) ?

The solution to log_{10}(K)+3log_{10}(L)-5log_{10}(T) is log_{10}((KL^3)/(T^5))

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simplify log_{10}(K)+3log_{10}(L)-5log_{10}(T)

simplify

lo g_{10} (K) + 3 lo g_{10} (L) - 5 lo g_{10} (T)

lo g_{10} (\frac{K L ^{3}}{T ^{5}})

Solution steps

lo g_{10} (K) + 3 lo g_{10} (L) - 5 lo g_{10} (T)

Apply log rule:

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

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

= lo g_{10} (K) + lo g_{10} (L^{3}) - 5 lo g_{10} (T)

Apply log rule:

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

lo g_{10} (K) + lo g_{10} (L^{3}) = lo g_{10} (L^{3} K)

= lo g_{10} (K L^{3}) - 5 lo g_{10} (T)

Apply log rule:

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

5 lo g_{10} (T) = lo g_{10} (T^{5})

= lo g_{10} (L^{3} K) - lo g_{10} (T^{5})

Apply log rule:

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

lo g_{10} (L^{3} K) - lo g_{10} (T^{5}) = lo g_{10} (\frac{L ^{3} K}{T ^{5}})

= lo g_{10} (\frac{K L ^{3}}{T ^{5}})

10 \cdot lo g_{10} (\frac{5 \cdot 1 0 ^{- 3}}{1})

3 lo g_{6} (x) - \frac{1}{5} lo g_{6} (y) + 2 lo g_{6} (w)

- 100 ln (5) + 100 ln (6)

ln (\frac{2.43 x + a}{x})

\frac{1}{4} ln (10) + ln (5) - \frac{1}{2} ln (7)

What is log_{10}(K)+3log_{10}(L)-5log_{10}(T) ?
The solution to log_{10}(K)+3log_{10}(L)-5log_{10}(T) is log_{10}((KL^3)/(T^5))