What is 2log_{a}(x^4)+4log_{a}(2x^2) ?

The solution to 2log_{a}(x^4)+4log_{a}(2x^2) is log_{a}(16x^{16})

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simplify 2log_{a}(x^4)+4log_{a}(2x^2)

simplify

2 lo g_{a} (x^{4}) + 4 lo g_{a} (2 x^{2})

lo g_{a} (16 x^{16})

Solution steps

2 lo g_{a} (x^{4}) + 4 lo g_{a} (2 x^{2})

Simplify

2 lo g_{a} (x^{4}) : 8 lo g_{a} (x)

= 8 lo g_{a} (x) + 4 lo g_{a} (2 x^{2})

8 lo g_{a} (x) = lo g_{a} (x^{8})

4 lo g_{a} (2 x^{2}) = lo g_{a} ((2 x^{2})^{4})

= lo g_{a} (x^{8}) + lo g_{a} ((2 x^{2})^{4})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{a} (x^{8}) + lo g_{a} ((2 x^{2})^{4}) = lo g_{a} (x^{8} (2 x^{2})^{4})

= lo g_{a} (x^{8} (2 x^{2})^{4})

Simplify

x^{8} (2 x^{2})^{4} : 16 x^{16}

= lo g_{a} (16 x^{16})

ln (x^{3} \cdot y^{2})

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ln ((1 + x^{2})^{c o s (x)})

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

lo g_{3} (a) + lo g_{3} (a + 3)

What is 2log_{a}(x^4)+4log_{a}(2x^2) ?
The solution to 2log_{a}(x^4)+4log_{a}(2x^2) is log_{a}(16x^{16})