What is expand log_{sqrt(2)}(4x^3) ?

The solution to expand log_{sqrt(2)}(4x^3) is 4+6log_{2}(x)

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expand log_{sqrt(2)}(4x^3)

expand

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

4 + 6 lo g_{2} (x)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{2} (4) = 2 lo g_{2} (4)

3 lo g_{2} (x) = 6 lo g_{2} (x)

= 2 lo g_{2} (4) + 6 lo g_{2} (x)

2 lo g_{2} (4) = 4

= 4 + 6 lo g_{2} (x)

lo g_{10} (- 2 x)

lo g_{3} (\frac{a b}{12})

2 ln (y) + 3 ln (5 y)

ln (x + h) - ln (x)

ln (\frac{3 x}{7})

What is expand log_{sqrt(2)}(4x^3) ?
The solution to expand log_{sqrt(2)}(4x^3) is 4+6log_{2}(x)