en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{10}(9)(27)

Solution

simplify

lo g_{10} (9) (27)

Solution

54 lo g_{10} (3)

+1

Solution steps

lo g_{10} (9) (27)

Apply rule:

(a) = a

(27) = 27

= lo g_{10} (9) \cdot 27

Factor the number:

9 = 3^{2}

= lo g_{10} (3^{2}) \cdot 27

Apply log rule:

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

lo g_{10} (3^{2}) = 2 lo g_{10} (3)

= 2 lo g_{10} (3) \cdot 27

Multiply the numbers:

2 \cdot 27 = 54

= 54 lo g_{10} (3)

Popular Examples

simplify log_{4}(16sqrt(4))simplify

lo g_{4} (164)

simplify 6sqrt(180)simplify

6180

simplify (1.2)/(1.8*10^{-3)}simplify

\frac{1.2}{1.8 \cdot 1 0 ^{- 3}}

simplify x^3y^3sqrt(25x^2y^5)simplify

x^{3} y^{3} 25 x^{2} y^{5}

simplify 8+10 simplify

8 + 10

Frequently Asked Questions (FAQ)

What is log_{10}(9)(27) ?
The solution to log_{10}(9)(27) is 54log_{10}(3)