What is log_{10}(b/c)+log_{10}(bc) ?

The solution to log_{10}(b/c)+log_{10}(bc) is 2log_{10}(b)

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simplify log_{10}(b/c)+log_{10}(bc)

simplify

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

2 lo g_{10} (b)

Solution steps

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

Apply log rule:

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

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

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

Simplify

\frac{b}{c} b c : b^{2}

= lo g_{10} (b^{2})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{10} (b^{2}) = 2 lo g_{10} (b)

= 2 lo g_{10} (b)

- lo g_{10} (2.8 \cdot 1 0^{- 10})

x - 2 lo g_{7} (7 x - 5)

lo g_{10} (\frac{x + 5}{x - 1})

lo g_{a} (x^{2} y^{3})

lo g_{10} (\frac{9 z}{3})

What is log_{10}(b/c)+log_{10}(bc) ?
The solution to log_{10}(b/c)+log_{10}(bc) is 2log_{10}(b)