What is expand log_{3}(81x^3sqrt(1+x^2)) ?

The solution to expand log_{3}(81x^3sqrt(1+x^2)) is 4+3log_{3}(x)+log_{3}(sqrt(1+x^2))

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expand log_{3}(81x^3sqrt(1+x^2))

expand

lo g_{3} (81 x^{3} 1 + x^{2})

4 + 3 lo g_{3} (x) + lo g_{3} (1 + x^{2})

Solution steps

lo g_{3} (81 x^{3} 1 + x^{2})

Apply log rule:

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

lo g_{3} (81 x^{3} 1 + x^{2}) = lo g_{3} (81) + lo g_{3} (x^{3}) + lo g_{3} (1 + x^{2})

= lo g_{3} (81) + lo g_{3} (x^{3}) + lo g_{3} (x^{2} + 1)

Apply log rule:

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

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

= lo g_{3} (81) + 3 lo g_{3} (x) + lo g_{3} (1 + x^{2})

lo g_{3} (81) = 4

= 4 + 3 lo g_{3} (x) + lo g_{3} (x^{2} + 1)

lo g_{4} (x y^{4} z^{4})

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

lo g_{6} (60) - lo g_{6} (30)

lo g_{b} (u^{2} v^{9})

lo g_{2} (\frac{x ^{9}}{5 y})

What is expand log_{3}(81x^3sqrt(1+x^2)) ?
The solution to expand log_{3}(81x^3sqrt(1+x^2)) is 4+3log_{3}(x)+log_{3}(sqrt(1+x^2))