What is 2.69-(0.02569)/2 ln((0.4^3)/(2^2)) ?

The solution to 2.69-(0.02569)/2 ln((0.4^3)/(2^2)) is 2.69-(0.07707)/2 ln(0.4)+0.02569ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2.69-(0.02569)/2 ln((0.4^3)/(2^2))

simplify

2.69 - \frac{0.02569}{2} ln (\frac{0. 4 ^{3}}{2 ^{2}})

2.69 - \frac{0.07707}{2} ln (0.4) + 0.02569 ln (2)

Decimal Notation

2.74311 \dots

Solution steps

2.69 - \frac{0.02569}{2} ln (\frac{0. 4 ^{3}}{2 ^{2}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{0. 4 ^{3}}{2 ^{2}}) = ln (0. 4^{3}) - ln (2^{2})

= 2.69 - \frac{0.02569}{2} (ln (0. 4^{3}) - ln (2^{2}))

Apply log rule:

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

ln (0. 4^{3}) = 3 ln (0.4)

= 2.69 - \frac{0.02569}{2} (3 ln (0.4) - ln (2^{2}))

Apply log rule:

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

ln (2^{2}) = 2 ln (2)

= 2.69 - \frac{0.02569}{2} (3 ln (0.4) - 2 ln (2))

Expand

- \frac{0.02569}{2} (3 ln (0.4) - 2 ln (2)) : - \frac{0.07707}{2} ln (0.4) + 0.02569 ln (2)

= 2.69 - \frac{0.07707}{2} ln (0.4) + 0.02569 ln (2)

\frac{1}{3} ln (5)

- (- \frac{1}{3} ln (5 + 1) + \frac{1}{3} ln (5 - 2))

ln (\frac{y}{2})

lo g_{10} (\frac{1}{4 \cdot 1 0 ^{- 10}})

ln (\frac{y ^{3} \cdot x ^{2} \cdot y ^{2}}{x ^{(\frac{1}{3})}})

What is 2.69-(0.02569)/2 ln((0.4^3)/(2^2)) ?
The solution to 2.69-(0.02569)/2 ln((0.4^3)/(2^2)) is 2.69-(0.07707)/2 ln(0.4)+0.02569ln(2)