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Popular >

simplify log_{sqrt(3)}(3x)

Solution

simplify

lo g_{3} (3 x)

Solution

2 + 2 lo g_{3} (x)

Solution steps

lo g_{3} (3 x)

Apply radical rule:

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

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

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

Apply log rule:

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

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

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

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

= 2 lo g_{3} (3 x)

Simplify

lo g_{3} (3 x) : 1 + lo g_{3} (x)

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

Expand

2 (1 + lo g_{3} (x)) : 2 + 2 lo g_{3} (x)

= 2 + 2 lo g_{3} (x)

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Frequently Asked Questions (FAQ)

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