What is log_{10}(a/(b^2c)) ?

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

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simplify log_{10}(a/(b^2c))

simplify

lo g_{10} (\frac{a}{b ^{2} c})

lo g_{10} (a) - 2 lo g_{10} (b) - lo g_{10} (c)

Solution steps

lo g_{10} (\frac{a}{b ^{2} c})

Apply log rule:

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

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

= lo g_{10} (a) - lo g_{10} (b^{2} c)

Simplify

lo g_{10} (b^{2} c) : 2 lo g_{10} (b) + lo g_{10} (c)

= lo g_{10} (a) - (2 lo g_{10} (b) + lo g_{10} (c))

Apply the distributive law:

- (a + b) = - a - b

- (2 lo g_{10} (b) + lo g_{10} (c)) = - 2 lo g_{10} (b) - lo g_{10} (c)

= lo g_{10} (a) - 2 lo g_{10} (b) - lo g_{10} (c)

lo g_{10} (x^{2} - 5 x - 14) - lo g_{10} (x^{2} - 4)

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

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

lo g_{10} (x \cdot y \cdot z^{2})

lo g_{b} (u^{2} v)

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