What is log_{10}((a^2sqrt(ab))/((ab)^2)) ?

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

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simplify log_{10}((a^2sqrt(ab))/((ab)^2))

simplify

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

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

Solution steps

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

Cancel

\frac{a ^{2} ab}{( ab ) ^{2}} : \frac{a}{b b}

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (b b) : lo g_{10} (b) + lo g_{10} (b)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

2 lo g_{10} (x) - 8 lo g_{10} (y)

- lo g_{10} (2 \cdot 1 0^{- 2})

- 1 - lo g_{\frac{1}{3}} (x) - lo g_{\frac{1}{3}} (x + 2)

2 ln (3) + ln (5)

lo g_{10} (\frac{x ^{2} y ^{5}}{z})

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