What is ln(7+sqrt(41))-2ln(2) ?

The solution to ln(7+sqrt(41))-2ln(2) is ln((7+sqrt(41))/4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(7+sqrt(41))-2ln(2)

simplify

ln (7 + 41) - 2 ln (2)

ln (\frac{7 + 41}{4})

Decimal Notation

1.20919 \dots

Solution steps

ln (7 + 41) - 2 ln (2)

Apply log rule:

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

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

= ln (7 + 41) - ln (2^{2})

Apply log rule:

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

ln (7 + 41) - ln (2^{2}) = ln (\frac{7 + 41}{2 ^{2}})

= ln (\frac{7 + 41}{2 ^{2}})

2^{2} = 4

= ln (\frac{7 + 41}{4})

lo g_{3} (8) + lo g_{3} (4)

- \frac{3}{5} \cdot lo g_{2} (\frac{3}{5}) - \frac{2}{5} \cdot lo g_{2} (\frac{2}{5})

lo g_{10} (\frac{x ^{9}}{y ^{4}})

lo g_{10} (\frac{x}{y})

ln (\frac{25}{9})

What is ln(7+sqrt(41))-2ln(2) ?
The solution to ln(7+sqrt(41))-2ln(2) is ln((7+sqrt(41))/4)