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Popular >

simplify log_{sqrt(2)}(3)

Solution

simplify

lo g_{2} (3)

Solution

2 lo g_{2} (3)

+1

Decimal Notation

3.16992 \dots

Solution steps

lo g_{2} (3)

Apply radical rule:

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

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

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

Apply log rule:

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

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

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

\frac{1}{\frac{1}{2}} = 2

= 2 lo g_{2} (3)

Popular Examples

\frac{3}{2 x + 5} - x > 0

simplify (x^2)(x^{-1/2})simplify

(x^{2}) (x^{- \frac{1}{2}})

(2a-3)/3 =(4a+2)/4

\frac{2 a - 3}{3} = \frac{4 a + 2}{4}

x^{2} + 7 x + 10 \leq 0

(2x^2)/3-x<(8x)/3 (1+x)+1

\frac{2 x ^{2}}{3} - x < \frac{8 x}{3} (1 + x) + 1

Frequently Asked Questions (FAQ)

What is log_{sqrt(2)}(3) ?
The solution to log_{sqrt(2)}(3) is 2log_{2}(3)