en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{27}(81)

Solution

simplify

lo g_{27} (81)

Solution

\frac{4}{3}

+1

Decimal Notation

1.33333 \dots

Solution steps

lo g_{27} (81)

Factor the number:

27 = 3^{3}

= lo g_{3^{3}} (81)

Apply log rule:

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

lo g_{3^{3}} (81) = \frac{1}{3} lo g_{3} (81)

= \frac{1}{3} lo g_{3} (81)

Factor the number:

81 = 3^{4}

= \frac{1}{3} lo g_{3} (3^{4})

Apply log rule:

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

lo g_{3} (3^{4}) = 4

= \frac{1}{3} \cdot 4

\frac{1}{3} \cdot 4 = \frac{4}{3}

= \frac{4}{3}

Popular Examples

simplify (4/3)^1 simplify

(\frac{4}{3})^{1}

- 4 g^{2} - 68 g = 172

x^{2} - 9 x + 5 = 0

simplify (e^{-3x})^2 simplify

(e^{- 3 x})^{2}

simplify (6-2i)(6+2i)simplify

(6 - 2 i) (6 + 2 i)

Frequently Asked Questions (FAQ)

What is log_{27}(81) ?
The solution to log_{27}(81) is 4/3