What is 1/2 log_{3}(5x) ?

The solution to 1/2 log_{3}(5x) is 1/2 log_{3}(5)+1/2 log_{3}(x)

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simplify 1/2 log_{3}(5x)

simplify

\frac{1}{2} lo g_{3} (5 x)

\frac{1}{2} lo g_{3} (5) + \frac{1}{2} lo g_{3} (x)

Solution steps

\frac{1}{2} 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}{2} (lo g_{3} (5) + lo g_{3} (x))

Apply the distributive law:

a (b + c) = ab + a c

\frac{1}{2} (lo g_{3} (5) + lo g_{3} (x)) = \frac{1}{2} lo g_{3} (5) + \frac{1}{2} lo g_{3} (x)

= \frac{1}{2} lo g_{3} (5) + \frac{1}{2} lo g_{3} (x)

\frac{1}{3} (3 lo g_{7} (a) + 2 lo g_{7} (b))

\frac{2}{3} ln (8) - 2 ln (4) + ln (24)

[\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]

lo g_{2} (10) + lo g_{2} (20)

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

What is 1/2 log_{3}(5x) ?
The solution to 1/2 log_{3}(5x) is 1/2 log_{3}(5)+1/2 log_{3}(x)