What is 1/4 log_{3}(5x) ?

The solution to 1/4 log_{3}(5x) is 1/4 log_{3}(5)+1/4 log_{3}(x)

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simplify 1/4 log_{3}(5x)

simplify

\frac{1}{4} lo g_{3} (5 x)

\frac{1}{4} lo g_{3} (5) + \frac{1}{4} lo g_{3} (x)

Solution steps

\frac{1}{4} lo g_{3} (5 x)

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{3} (5 x) = lo g_{3} (5) + lo g_{3} (x)

= \frac{1}{4} (lo g_{3} (5) + lo g_{3} (x))

Apply the distributive law:

a (b + c) = ab + a c

\frac{1}{4} (lo g_{3} (5) + lo g_{3} (x)) = \frac{1}{4} lo g_{3} (5) + \frac{1}{4} lo g_{3} (x)

= \frac{1}{4} lo g_{3} (5) + \frac{1}{4} lo g_{3} (x)

lo g_{4} (x) + lo g_{4} (36)

ln (\frac{26}{25})

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

lo g_{b} (\frac{x y ^{4}}{z ^{4}})

What is 1/4 log_{3}(5x) ?
The solution to 1/4 log_{3}(5x) is 1/4 log_{3}(5)+1/4 log_{3}(x)