What is log_{10}((a^2)/(bc^3)) ?

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

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simplify log_{10}((a^2)/(bc^3))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{10} (a^{2}) = 2 lo g_{10} (a)

lo g_{10} (b c^{3}) = lo g_{10} (b) + 3 lo g_{10} (c)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

lo g_{10} (m \cdot n \cdot p \cdot q)

- (2 ln (3) + ln (2))

\frac{3}{2} (ln (13) - ln (8))

ln (4) + \frac{1}{3} ln (27)

3 ln (4 x)

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