What is ln(1/(e^{20)}-1)-ln(20)(1/2) ?

The solution to ln(1/(e^{20)}-1)-ln(20)(1/2) is ln((sqrt(5)(1-e^{20}))/(10e^{20)})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(1/(e^{20)}-1)-ln(20)(1/2)

simplify

ln (\frac{1}{e ^{20}} - 1) - ln (20) (\frac{1}{2})

ln (\frac{5 ( 1 - e ^{20} )}{10 e ^{20}})

Solution steps

ln (\frac{1}{e ^{20}} - 1) - ln (20) (\frac{1}{2})

Apply log rule:

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

(\frac{1}{2}) ln (20) = ln (2 0^{(\frac{1}{2})})

= ln (\frac{1}{e ^{20}} - 1) - ln (2 0^{(\frac{1}{2})})

Apply log rule:

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

ln (\frac{1}{e ^{20}} - 1) - ln (2 0^{(\frac{1}{2})}) = ln (\frac{\frac{1}{e ^{20}} - 1}{2 0 ^{\frac{1}{2}}})

= ln (\frac{\frac{1}{e ^{20}} - 1}{2 0 ^{\frac{1}{2}}})

\frac{\frac{1}{e ^{20}} - 1}{2 0 ^{(\frac{1}{2})}} = \frac{5 ( 1 - e ^{20} )}{10 e ^{20}}

= ln (\frac{5 ( 1 - e ^{20} )}{10 e ^{20}})

\frac{2 \cdot 0.053}{5} \cdot ln (\frac{0.45}{0.2})

- lo g_{10} (2.43 \cdot 1 0^{- 4})

\frac{ln ( 10 ) - ln ( 3 )}{2 ln ( 3 )}

ln (- α (x - θ)^{2})

ln (cos (a) rc t an x)

What is ln(1/(e^{20)}-1)-ln(20)(1/2) ?
The solution to ln(1/(e^{20)}-1)-ln(20)(1/2) is ln((sqrt(5)(1-e^{20}))/(10e^{20)})