en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{1/2}(sqrt(128))

Solution

simplify

lo g_{\frac{1}{2}} (128)

Solution

- \frac{7}{2}

+1

Decimal Notation

- 3.5

Solution steps

lo g_{\frac{1}{2}} (128)

Apply log rule:

lo g_{\frac{1}{a}} (x) = - lo g_{a} (x)

lo g_{\frac{1}{2}} (128) = - lo g_{2} (128)

= - lo g_{2} (128)

128 = 2^{\frac{7}{2}}

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

Apply log rule:

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

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

= - \frac{7}{2}

Popular Examples

expand (a^7-b^7)^2 expand

(a^{7} - b^{7})^{2}

simplify 2/3+5/4 simplify

\frac{2}{3} + \frac{5}{4}

expand (9-x^2)^2 expand

(9 - x^{2})^{2}

simplify-x-2x simplify

- x - 2 x

simplify-2^7 simplify

- 2^{7}

Frequently Asked Questions (FAQ)

What is log_{1/2}(sqrt(128)) ?
The solution to log_{1/2}(sqrt(128)) is -7/2