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

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

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

expand

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

4 + 8 lo g_{3} (x)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= lo g_{3} (9) + 4 lo g_{3} (x)

lo g_{3} (9) = 2 lo g_{3} (9)

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

= 2 lo g_{3} (9) + 8 lo g_{3} (x)

2 lo g_{3} (9) = 4

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

ln (x^{2} - 3 x - 4) - ln (x - 4) + ln (x + 1)

lo g_{4} (13 b^{2} c)

ln (2 \cdot 3)

ln (x^{2} - 5 x + 6) - ln (x^{2} - 4) + ln (x + 2)

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