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Popular >

simplify log_{5}(75)

Solution

simplify

lo g_{5} (75)

Solution

2 + lo g_{5} (3)

+1

Decimal Notation

2.68260 \dots

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)

Popular Examples

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2 + \frac{9}{2}

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(\frac{b}{2 a})^{2}

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(7 x - 5) - (3 x - 2)

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5 - 11 (- 1)

simplify (2)^{5/2}simplify

(2)^{\frac{5}{2}}

Frequently Asked Questions (FAQ)

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