What is log_{10}((a^6)/(b^5sqrt(c))) ?

The solution to log_{10}((a^6)/(b^5sqrt(c))) is 6log_{10}(a)-5log_{10}(b)-log_{10}(sqrt(c))

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simplify log_{10}((a^6)/(b^5sqrt(c)))

simplify

lo g_{10} (\frac{a ^{6}}{b ^{5} c})

6 lo g_{10} (a) - 5 lo g_{10} (b) - lo g_{10} (c)

Solution steps

lo g_{10} (\frac{a ^{6}}{b ^{5} c})

Apply log rule:

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

lo g_{10} (\frac{a ^{6}}{b ^{5} c}) = lo g_{10} (a^{6}) - lo g_{10} (b^{5} c)

= lo g_{10} (a^{6}) - lo g_{10} (b^{5} c)

lo g_{10} (a^{6}) = 6 lo g_{10} (a)

lo g_{10} (b^{5} c) = 5 lo g_{10} (b) + lo g_{10} (c)

= 6 lo g_{10} (a) - (5 lo g_{10} (b) + lo g_{10} (c))

Apply the distributive law:

- (a + b) = - a - b

- (5 lo g_{10} (b) + lo g_{10} (c)) = - 5 lo g_{10} (b) - lo g_{10} (c)

= 6 lo g_{10} (a) - 5 lo g_{10} (b) - lo g_{10} (c)

lo g_{10} (5) + lo g_{10} (x)

lo g_{3} (4 x^{2} y) + lo g_{3} (5 x^{3} y^{2})

lo g_{10} (- \frac{1}{2} x) + 1

lo g_{10} (\frac{y}{x ^{3}})

lo g_{10} (24) - lo g_{10} (8)

What is log_{10}((a^6)/(b^5sqrt(c))) ?
The solution to log_{10}((a^6)/(b^5sqrt(c))) is 6log_{10}(a)-5log_{10}(b)-log_{10}(sqrt(c))