What is ln(4sqrt(2))+i(45+2kpi) ?

The solution to ln(4sqrt(2))+i(45+2kpi) is (5ln(2))/2+i(45+2pik)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(4sqrt(2))+i(45+2kpi)

simplify

ln (42) + i (4 5^{\circ} + 2 kπ)

\frac{5 ln ( 2 )}{2} + i (4 5^{\circ} + 2 πk)

Solution steps

ln (42) + i (4 5^{\circ} + 2 kπ)

Apply log rule:

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

ln (42) = ln (4) + ln (2)

= ln (4) + ln (2) + i (2 πk + 4 5^{\circ})

ln (2) = \frac{1}{2} ln (2)

= ln (4) + \frac{1}{2} ln (2) + i (2 πk + 4 5^{\circ})

ln (4) = 2 ln (2)

= 2 ln (2) + \frac{1}{2} ln (2) + i (2 πk + 4 5^{\circ})

= 2 ln (2) + \frac{1}{2} ln (2) + i (4 5^{\circ} + 2 πk)

Expand

i (4 5^{\circ} + 2 kπ) : 4 5^{\circ} i + 2 iπk

= 2 ln (2) + \frac{1}{2} ln (2) + 4 5^{\circ} i + 2 iπk

Add similar elements:

2 ln (2) + \frac{1}{2} ln (2) = \frac{5}{2} ln (2)

= \frac{5}{2} ln (2) + 4 5^{\circ} i + 2 iπk

Rewrite

\frac{5}{2} ln (2) + 4 5^{\circ} i + 2 iπk

in standard complex form:

\frac{5 ln ( 2 )}{2} + (4 5^{\circ} + 2 πk) i

= \frac{5 ln ( 2 )}{2} + (4 5^{\circ} + 2 πk) i

ln (21) - ln (18.5)

- lo g_{10} (5 \cdot 1 0^{- 15})

lo g_{10} (z x^{5})

2 ln \frac{1}{2} - ln \frac{3}{4}

lo g_{b} ((\frac{x ^{4}}{y ^{3} z ^{2}})^{- 5})

What is ln(4sqrt(2))+i(45+2kpi) ?
The solution to ln(4sqrt(2))+i(45+2kpi) is (5ln(2))/2+i(45+2pik)