What is expand log_{10}((x^2+y^4)^3) ?

The solution to expand log_{10}((x^2+y^4)^3) is 3log_{10}(x^2+y^4)

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expand log_{10}((x^2+y^4)^3)

expand

lo g_{10} ((x^{2} + y^{4})^{3})

3 lo g_{10} (x^{2} + y^{4})

Solution steps

lo g_{10} ((x^{2} + y^{4})^{3})

Apply log rule:

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

lo g_{10} ((x^{2} + y^{4})^{3}) = 3 lo g_{10} (x^{2} + y^{4})

= 3 lo g_{10} (x^{2} + y^{4})

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

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

lo g_{3} (10 x) - lo g_{3} (2)

2 lo g_{3} (r) + lo g_{3} (s)

- 10 ln (16) + 10 ln (9)

What is expand log_{10}((x^2+y^4)^3) ?
The solution to expand log_{10}((x^2+y^4)^3) is 3log_{10}(x^2+y^4)