What is 5log_{2}(x)+5log_{2}(y) ?

The solution to 5log_{2}(x)+5log_{2}(y) is log_{2}(x^5y^5)

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simplify 5log_{2}(x)+5log_{2}(y)

simplify

5 lo g_{2} (x) + 5 lo g_{2} (y)

lo g_{2} (x^{5} y^{5})

Solution steps

5 lo g_{2} (x) + 5 lo g_{2} (y)

Apply log rule:

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

5 lo g_{2} (x) = lo g_{2} (x^{5})

= lo g_{2} (x^{5}) + 5 lo g_{2} (y)

Apply log rule:

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

5 lo g_{2} (y) = lo g_{2} (y^{5})

= lo g_{2} (x^{5}) + lo g_{2} (y^{5})

Apply log rule:

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

lo g_{2} (x^{5}) + lo g_{2} (y^{5}) = lo g_{2} (x^{5} y^{5})

= lo g_{2} (x^{5} y^{5})

9 lo g_{10} (2^{2}) - 9 lo g_{10} (5^{2})

lo g_{3} (7) - lo g_{3} (10)

lo g_{6} (x) - lo g_{6} (x^{8})

3 lo g_{3} (a) + 2 lo g_{3} (3) - lo g_{3} (c)

lo g_{2} (a) - lo g_{2} (b) - lo g_{2} (c)

What is 5log_{2}(x)+5log_{2}(y) ?
The solution to 5log_{2}(x)+5log_{2}(y) is log_{2}(x^5y^5)