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

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

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simplify 2log_{2}(x)+4log_{2}(y)

simplify

2 lo g_{2} (x) + 4 lo g_{2} (y)

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

Solution steps

2 lo g_{2} (x) + 4 lo g_{2} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

(lo g_{10} (6) + lo g_{10} (4)) - lo g_{10} (3)

2 lo g_{10} (5) - 6 lo g_{10} (3)

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

(\frac{1}{e})^{2} lo g_{3} (\frac{1}{e})

4 lo g_{10} (3) + 1 lo g_{10} (x)

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