What is log_{5}((5a)/(bc)) ?

The solution to log_{5}((5a)/(bc)) is 1+log_{5}(a)-log_{5}(b)-log_{5}(c)

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simplify log_{5}((5a)/(bc))

simplify

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

1 + lo g_{5} (a) - lo g_{5} (b) - lo g_{5} (c)

Solution steps

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

Apply log rule:

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

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

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

lo g_{5} (5 a) = 1 + lo g_{5} (a)

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

= 1 + lo g_{5} (a) - (lo g_{5} (b) + lo g_{5} (c))

Apply the distributive law:

- (a + b) = - a - b

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

= 1 + lo g_{5} (a) - lo g_{5} (b) - lo g_{5} (c)

lo g_{a} (\frac{3 x}{8 n})

ln (\frac{9}{4 x ^{4} y})

ln (5) + ln (7) + 2 ln (6)

6 ln (x) - \frac{1}{4} ln (y)

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

What is log_{5}((5a)/(bc)) ?
The solution to log_{5}((5a)/(bc)) is 1+log_{5}(a)-log_{5}(b)-log_{5}(c)