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Popular >

simplify log_{5}(75)

Solution

simplify

lo g_{5} (75)

Solution

2 + lo g_{5} (3)

+1

Solution steps

lo g_{5} (75)

Factor the number:

75 = 5^{2} \cdot 3

= lo g_{5} (5^{2} \cdot 3)

Apply log rule:

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

lo g_{5} (5^{2} \cdot 3) = lo g_{5} (5^{2}) + lo g_{5} (3)

= lo g_{5} (5^{2}) + lo g_{5} (3)

Apply log rule:

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

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

= 2 + lo g_{5} (3)

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Frequently Asked Questions (FAQ)

What is log_{5}(75) ?
The solution to log_{5}(75) is 2+log_{5}(3)