What is ln(1+sqrt(2))*1/(sqrt(2))-ln(-1sqrt(2)) ?

The solution to ln(1+sqrt(2))*1/(sqrt(2))-ln(-1sqrt(2)) is ln(-sqrt(((1+\sqrt{2))^{sqrt(2)})/2})

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simplify ln(1+sqrt(2))*1/(sqrt(2))-ln(-1sqrt(2))

simplify

ln (1 + 2) \cdot \frac{1}{2} - ln (- 12)

ln - \frac{( 1 + 2 ) ^{2}}{2}

Decimal Notation

0.27665 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{( 1 + 2 ) ^{\frac{1}{2}}}{- 1 \cdot 2} = - \frac{( 1 + 2 ) ^{\frac{2}{2}}}{2}

= ln - \frac{( 1 + 2 ) ^{\frac{2}{2}}}{2}

\frac{( 1 + 2 ) ^{\frac{2}{2}}}{2} = \frac{( 1 + 2 ) ^{2}}{2}

= ln - \frac{( 1 + 2 ) ^{2}}{2}

2 ln (x + 3) - 5 ln (x) + 4 ln (3 x + 1)

- lo g_{10} (3.60555 \cdot 1 0^{- 6})

ln (\frac{70}{53.3})

- lo g_{10} (1.65 \cdot 1 0^{- 5})

ln (\frac{x ^{2} - y ^{2}}{x ^{2} + y ^{2}})

What is ln(1+sqrt(2))*1/(sqrt(2))-ln(-1sqrt(2)) ?
The solution to ln(1+sqrt(2))*1/(sqrt(2))-ln(-1sqrt(2)) is ln(-sqrt(((1+\sqrt{2))^{sqrt(2)})/2})