What is log_{sqrt(3)}(\sqrt[4]{3}) ?

The solution to log_{sqrt(3)}(\sqrt[4]{3}) is 1/2

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simplify log_{sqrt(3)}(\sqrt[4]{3})

simplify

\frac{1}{2}

Decimal Notation

0.5

Solution steps

Apply radical rule:

a = a^{\frac{1}{2}}

3 = 3^{\frac{1}{2}}

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

Apply radical rule:

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

Apply log rule:

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

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

= \frac{1}{\frac{1}{2}} \cdot \frac{1}{4}

\frac{1}{\frac{1}{2}} \cdot \frac{1}{4} = \frac{1}{2}

= \frac{1}{2}

- 2 a x - 2 a y - ab x - ab y

\frac{6 x + 20}{2 x + 10}

- \frac{46}{17} - 3

(3 - 4 i) (3 - 4 i)

3 (2 y - 7) + 4 y

What is log_{sqrt(3)}(\sqrt[4]{3}) ?
The solution to log_{sqrt(3)}(\sqrt[4]{3}) is 1/2