What is log_{10}((a^3)/(b^2*sqrt(2))) ?

The solution to log_{10}((a^3)/(b^2*sqrt(2))) is 3log_{10}(a)-2log_{10}(b)-log_{10}(sqrt(2))

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simplify log_{10}((a^3)/(b^2*sqrt(2)))

simplify

lo g_{10} (\frac{a ^{3}}{b ^{2} \cdot 2})

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

Solution steps

lo g_{10} (\frac{a ^{3}}{b ^{2} 2})

Apply log rule:

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

lo g_{10} (\frac{a ^{3}}{b ^{2} 2}) = lo g_{10} (a^{3}) - lo g_{10} (b^{2} 2)

= lo g_{10} (a^{3}) - lo g_{10} (b^{2} 2)

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

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

= 3 lo g_{10} (a) - (2 lo g_{10} (b) + lo g_{10} (2))

Apply the distributive law:

- (a + b) = - a - b

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

= 3 lo g_{10} (a) - 2 lo g_{10} (b) - lo g_{10} (2)

\frac{3}{5} lo g_{2} (\frac{3}{5}) + \frac{2}{5} lo g_{2} (\frac{2}{5})

lo g_{b} (\frac{x ^{2} y}{b ^{3}})

16.7 + 10 \cdot lo g_{10} (\frac{750}{100})

lo g_{4} (\frac{5 x y}{2 x + y})

lo g_{10} (16 x^{2})

What is log_{10}((a^3)/(b^2*sqrt(2))) ?
The solution to log_{10}((a^3)/(b^2*sqrt(2))) is 3log_{10}(a)-2log_{10}(b)-log_{10}(sqrt(2))