What is 1/3 log_{10}(a)-1/2 (log_{10}(b)-log_{10}(c)) ?

The solution to 1/3 log_{10}(a)-1/2 (log_{10}(b)-log_{10}(c)) is (log_{10}(a))/3-(log_{10}(b/c))/2

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simplify 1/3 log_{10}(a)-1/2 (log_{10}(b)-log_{10}(c))

simplify

\frac{1}{3} lo g_{10} (a) - \frac{1}{2} (lo g_{10} (b) - lo g_{10} (c))

\frac{lo g _{10} ( a )}{3} - \frac{lo g _{10} ( \frac{b}{c} )}{2}

Solution steps

\frac{1}{3} lo g_{10} (a) - \frac{1}{2} (lo g_{10} (b) - lo g_{10} (c))

Apply log rule:

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

lo g_{10} (b) - lo g_{10} (c) = lo g_{10} (\frac{b}{c})

= \frac{1}{3} lo g_{10} (a) - \frac{1}{2} lo g_{10} (\frac{b}{c})

\frac{1}{3} lo g_{10} (a) = \frac{lo g _{10} ( a )}{3}

\frac{1}{2} lo g_{10} (\frac{b}{c}) = \frac{lo g _{10} ( \frac{b}{c} )}{2}

= \frac{lo g _{10} ( a )}{3} - \frac{lo g _{10} ( \frac{b}{c} )}{2}

lo g_{2} (6) - lo g_{2} (15) - lo g_{2} (20)

lo g_{10} (4 x)

\frac{1}{2} + ln (\frac{1}{2})

lo g_{b} (m) + lo g_{b} (n)

\frac{1}{2} lo g_{10} (a) + 9 lo g_{10} (b)

What is 1/3 log_{10}(a)-1/2 (log_{10}(b)-log_{10}(c)) ?
The solution to 1/3 log_{10}(a)-1/2 (log_{10}(b)-log_{10}(c)) is (log_{10}(a))/3-(log_{10}(b/c))/2