en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{sqrt(2)}(32)

Solution

simplify

lo g_{2} (32)

Solution

10

Solution steps

lo g_{2} (32)

Apply radical rule:

a = a^{\frac{1}{2}}

2 = 2^{\frac{1}{2}}

= lo g_{2^{\frac{1}{2}}} (32)

Apply log rule:

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

lo g_{2^{\frac{1}{2}}} (32) = \frac{1}{\frac{1}{2}} lo g_{2} (32)

= \frac{1}{\frac{1}{2}} lo g_{2} (32)

Factor the number:

32 = 2^{5}

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

Apply log rule:

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

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

= \frac{1}{\frac{1}{2}} \cdot 5

\frac{1}{\frac{1}{2}} \cdot 5 = 10

= 10

Popular Examples

\frac{x}{4} = 2

\frac{v}{4} + 1 = - 3

simplify 1/7-10(53917.16333)simplify

\frac{1}{7} - 10 (53917.16333)

simplify (2pi)/(7/6)simplify

\frac{2 π}{\frac{7}{6}}

simplify (2i)^7 simplify

(2 i)^{7}

Frequently Asked Questions (FAQ)

What is log_{sqrt(2)}(32) ?
The solution to log_{sqrt(2)}(32) is 10