What is log_{10}(a)-log_{10}(b)+log_{10}(c) ?

The solution to log_{10}(a)-log_{10}(b)+log_{10}(c) is log_{10}((ac)/b)

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simplify log_{10}(a)-log_{10}(b)+log_{10}(c)

simplify

lo g_{10} (a) - lo g_{10} (b) + lo g_{10} (c)

lo g_{10} (\frac{a c}{b})

Solution steps

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

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

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

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

Simplify

\frac{a}{b} c : \frac{a c}{b}

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

lo g_{10} (3) + 2 lo g_{10} (2)

3 lo g_{10} (a) + 5 lo g_{10} (b) - lo g_{10} (ab)

lo g_{10} (5 \cdot 2)

lo g_{5} (\frac{x}{3 ^{2} z})

What is log_{10}(a)-log_{10}(b)+log_{10}(c) ?
The solution to log_{10}(a)-log_{10}(b)+log_{10}(c) is log_{10}((ac)/b)