en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 9^{log_{3}(2)}

Solution

simplify

9^{l o g_{3} (2)}

Solution

4

Solution steps

9^{l o g_{3} (2)}

Factor the number:

9 = 3^{2}

= (3^{2})^{l o g_{3} (2)}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 3^{2 l o g_{3} (2)}

Apply exponent rule:

a^{b c} = (a^{b})^{c}, a \geq 0

3^{2 l o g_{3} (2)} = (3^{l o g_{3} (2)})^{2}

= (3^{l o g_{3} (2)})^{2}

Apply log rule:

a^{l o g_{a} (b)} = b

3^{l o g_{3} (2)} = 2

= 2^{2}

2^{2} = 4

= 4

Popular Examples

simplify-14^2 simplify

- 1 4^{2}

simplify (x^6+6x^3-2x^5-7x^2-4x+6)/(x^4-3x^2+2)simplify

\frac{x ^{6} + 6 x ^{3} - 2 x ^{5} - 7 x ^{2} - 4 x + 6}{x ^{4} - 3 x ^{2} + 2}

simplify-5\times (-5)simplify

- 5 \times (- 5)

simplify (7+i)-(6-4i)simplify

(7 + i) - (6 - 4 i)

expand (5x+3)(5x-3)expand

(5 x + 3) (5 x - 3)

Frequently Asked Questions (FAQ)

What is 9^{log_{3}(2)} ?
The solution to 9^{log_{3}(2)} is 4