What is (10000)/(200pi^2)(ln((400)/(0.4))+ln(8)) ?

The solution to (10000)/(200pi^2)(ln((400)/(0.4))+ln(8)) is (150ln(20))/(pi^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (10000)/(200pi^2)(ln((400)/(0.4))+ln(8))

simplify

\frac{10000}{200 π ^{2}} (ln (\frac{400}{0.4}) + ln (8))

\frac{150 ln ( 20 )}{π ^{2}}

Decimal Notation

45.52967 \dots

Solution steps

\frac{10000}{200 π ^{2}} (ln (\frac{400}{0.4}) + ln (8))

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{400}{0.4}) + ln (8) = ln (8 \cdot \frac{400}{0.4})

= \frac{10000}{200 π ^{2}} ln (8 \cdot \frac{400}{0.4})

\frac{400}{0.4} \cdot 8 = 8000

= \frac{10000}{200 π ^{2}} ln (8000)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{10000 ln ( 8000 )}{200 π ^{2}}

Divide the numbers:

\frac{10000}{200} = 50

= \frac{50 ln ( 8000 )}{π ^{2}}

Simplify

ln (8000) : 3 ln (20)

= \frac{50 \cdot 3 ln ( 20 )}{π ^{2}}

Multiply the numbers:

50 \cdot 3 = 150

= \frac{150 ln ( 20 )}{π ^{2}}

6 ln (2 (0 + 1))

\frac{e ^{\frac{7}{4}}}{4} + ln (\frac{e ^{\frac{7}{4}}}{2})

0.0259 \cdot ln (\frac{2 \cdot 1 0 ^{16}}{1.5 \cdot 1 0 ^{10}})

\frac{1}{2} ln (2 \cdot 9.5 + 1) + 2 ln (9.5 - 1)

\frac{1}{0.0105} ln (\frac{8000}{5000})

What is (10000)/(200pi^2)(ln((400)/(0.4))+ln(8)) ?
The solution to (10000)/(200pi^2)(ln((400)/(0.4))+ln(8)) is (150ln(20))/(pi^2)