What is log_{10}((a^3)/(b^9sqrt(c))) ?

The solution to log_{10}((a^3)/(b^9sqrt(c))) is 3log_{10}(a)-9log_{10}(b)-log_{10}(sqrt(c))

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simplify log_{10}((a^3)/(b^9sqrt(c)))

simplify

lo g_{10} (\frac{a ^{3}}{b ^{9} c})

3 lo g_{10} (a) - 9 lo g_{10} (b) - lo g_{10} (c)

Solution steps

lo g_{10} (\frac{a ^{3}}{b ^{9} c})

Apply log rule:

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

lo g_{10} (\frac{a ^{3}}{b ^{9} c}) = lo g_{10} (a^{3}) - lo g_{10} (b^{9} c)

= lo g_{10} (a^{3}) - lo g_{10} (b^{9} c)

lo g_{10} (a^{3}) = 3 lo g_{10} (a)

lo g_{10} (b^{9} c) = 9 lo g_{10} (b) + lo g_{10} (c)

= 3 lo g_{10} (a) - (9 lo g_{10} (b) + lo g_{10} (c))

Apply the distributive law:

- (a + b) = - a - b

- (9 lo g_{10} (b) + lo g_{10} (c)) = - 9 lo g_{10} (b) - lo g_{10} (c)

= 3 lo g_{10} (a) - 9 lo g_{10} (b) - lo g_{10} (c)

2 lo g_{10} (21) - lo g_{10} (x)

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What is log_{10}((a^3)/(b^9sqrt(c))) ?
The solution to log_{10}((a^3)/(b^9sqrt(c))) is 3log_{10}(a)-9log_{10}(b)-log_{10}(sqrt(c))