What is log_{sqrt(3)}(9x^4) ?

The solution to log_{sqrt(3)}(9x^4) is 4+8log_{3}(x)

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simplify log_{sqrt(3)}(9x^4)

simplify

lo g_{3} (9 x^{4})

4 + 8 lo g_{3} (x)

Solution steps

lo g_{3} (9 x^{4})

Apply radical rule:

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

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

= lo g_{3^{\frac{1}{2}}} (9 x^{4})

Apply log rule:

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

lo g_{3^{\frac{1}{2}}} (9 x^{4}) = \frac{1}{\frac{1}{2}} lo g_{3} (9 x^{4})

= \frac{1}{\frac{1}{2}} lo g_{3} (9 x^{4})

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

= 2 lo g_{3} (9 x^{4})

Simplify

lo g_{3} (9 x^{4}) : 2 + 4 lo g_{3} (x)

= 2 (2 + 4 lo g_{3} (x))

Expand

2 (2 + 4 lo g_{3} (x)) : 4 + 8 lo g_{3} (x)

= 4 + 8 lo g_{3} (x)

3 \cdot lo g_{10} (2) + 2 \cdot lo g_{10} (3)

- 0.8 lo g_{2} (0.8) - 0.2 lo g_{2} (0.2)

f (x) = lo g_{10} (5 x + 4) - lo g_{10} (x)

2 lo g_{10} (x) + lo g_{10} (y)

lo g_{10} (\frac{pq}{r})

What is log_{sqrt(3)}(9x^4) ?
The solution to log_{sqrt(3)}(9x^4) is 4+8log_{3}(x)