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Popular >

simplify log_{9}(2187)

Solution

simplify

lo g_{9} (2187)

Solution

\frac{7}{2}

+1

Decimal Notation

3.5

Solution steps

lo g_{9} (2187)

Factor the number:

9 = 3^{2}

= lo g_{3^{2}} (2187)

Apply log rule:

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

lo g_{3^{2}} (2187) = \frac{1}{2} lo g_{3} (2187)

= \frac{1}{2} lo g_{3} (2187)

Factor the number:

2187 = 3^{7}

= \frac{1}{2} lo g_{3} (3^{7})

Apply log rule:

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

lo g_{3} (3^{7}) = 7

= \frac{1}{2} \cdot 7

\frac{1}{2} \cdot 7 = \frac{7}{2}

= \frac{7}{2}

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Frequently Asked Questions (FAQ)

What is log_{9}(2187) ?
The solution to log_{9}(2187) is 7/2