What is 1/3 log_{10}(27)-1/2 log_{10}(49) ?

The solution to 1/3 log_{10}(27)-1/2 log_{10}(49) is log_{10}(3/7)

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simplify 1/3 log_{10}(27)-1/2 log_{10}(49)

simplify

\frac{1}{3} lo g_{10} (27) - \frac{1}{2} lo g_{10} (49)

lo g_{10} (\frac{3}{7})

Decimal Notation

- 0.36797 \dots

Solution steps

\frac{1}{3} lo g_{10} (27) - \frac{1}{2} lo g_{10} (49)

\frac{1}{3} lo g_{10} (27) = lo g_{10} (3)

\frac{1}{2} lo g_{10} (49) = lo g_{10} (7)

= lo g_{10} (3) - lo g_{10} (7)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (3) - lo g_{10} (7) = lo g_{10} (\frac{3}{7})

= lo g_{10} (\frac{3}{7})

ln ((2) e^{7 b})

\frac{( \frac{- 6 l n ^{3} ( 2 ) + 13 l n ^{2} ( 2 ) + 18 l n ( x ) + 12}{16 l n ^{5} ( 2 )} )}{120}

lo g_{10} (310 z)

7 ln (219) + 18 - 7 ln (3) + 6

What is 1/3 log_{10}(27)-1/2 log_{10}(49) ?
The solution to 1/3 log_{10}(27)-1/2 log_{10}(49) is log_{10}(3/7)