What is 1/4 log_{3}(2)+1/4 log_{3}(x) ?

The solution to 1/4 log_{3}(2)+1/4 log_{3}(x) is log_{3}(2^{1/4}x^{1/4})

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simplify 1/4 log_{3}(2)+1/4 log_{3}(x)

simplify

\frac{1}{4} lo g_{3} (2) + \frac{1}{4} lo g_{3} (x)

lo g_{3} (2^{\frac{1}{4}} x^{\frac{1}{4}})

Solution steps

\frac{1}{4} lo g_{3} (2) + \frac{1}{4} lo g_{3} (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{4} lo g_{3} (2) = lo g_{3} (2^{\frac{1}{4}})

= lo g_{3} (2^{\frac{1}{4}}) + \frac{1}{4} lo g_{3} (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{3} (2^{\frac{1}{4}}) + lo g_{3} (x^{\frac{1}{4}})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{3} (2^{\frac{1}{4}}) + lo g_{3} (x^{\frac{1}{4}}) = lo g_{3} (2^{\frac{1}{4}} x^{\frac{1}{4}})

= lo g_{3} (2^{\frac{1}{4}} x^{\frac{1}{4}})

lo g_{2} (2 a)

3 ln (\frac{5}{7})

2 lo g_{3} (5) - lo g_{3} (2)

ln (\frac{x ^{8} p ^{7} q ^{9}}{e ^{9}})

- 2 ln ∣ x - 1 ∣ + 3 ln ∣ x - 2 ∣ + ln x^{2} + 1 + C

What is 1/4 log_{3}(2)+1/4 log_{3}(x) ?
The solution to 1/4 log_{3}(2)+1/4 log_{3}(x) is log_{3}(2^{1/4}x^{1/4})