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Popular >

simplify log_{9}(25)

Solution

simplify

lo g_{9} (25)

Solution

lo g_{3} (5)

+1

Decimal Notation

1.46497 \dots

Solution steps

lo g_{9} (25)

Factor the number:

25 = 5^{2}

= lo g_{9} (5^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{9} (5^{2}) = 2 lo g_{9} (5)

= 2 lo g_{9} (5)

Factor the number:

9 = 3^{2}

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

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{3^{2}} (5) = \frac{1}{2} lo g_{3} (5)

= 2 \cdot \frac{1}{2} lo g_{3} (5)

2 \cdot \frac{1}{2} lo g_{3} (5) = lo g_{3} (5)

= lo g_{3} (5)

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Frequently Asked Questions (FAQ)

What is log_{9}(25) ?
The solution to log_{9}(25) is log_{3}(5)