What is 1/2 ln|3+e^8|-ln(2) ?

The solution to 1/2 ln|3+e^8|-ln(2) is ln(((3+e^8)^{1/2})/2)

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simplify 1/2 ln|3+e^8|-ln(2)

simplify

\frac{1}{2} ln 3 + e^{8} - ln (2)

ln \frac{( 3 + e ^{8} ) ^{\frac{1}{2}}}{2}

Decimal Notation

3.30735 \dots

Solution steps

\frac{1}{2} ln 3 + e^{8} - ln (2)

Apply log rule:

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

\frac{1}{2} ln e^{8} + 3 = ln (e^{8} + 3^{\frac{1}{2}})

= ln (e^{8} + 3^{\frac{1}{2}}) - ln (2)

Apply log rule:

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

ln (3 + e^{8}^{\frac{1}{2}}) - ln (2) = ln \frac{e ^{8} + 3 ^{\frac{1}{2}}}{2}

= ln \frac{3 + e ^{8} ^{\frac{1}{2}}}{2}

3 + e^{8}^{\frac{1}{2}} = (3 + e^{8})^{\frac{1}{2}}

= ln \frac{( 3 + e ^{8} ) ^{\frac{1}{2}}}{2}

lo g_{z} (\frac{2 x}{3})

- lo g_{10} (3 \cdot 1 0^{- 3})

ln (2) - 3 ln (3)

\frac{1}{2} lo g_{c} (x) + 5 lo g_{c} (y) - 2 lo g_{c} (x)

What is 1/2 ln|3+e^8|-ln(2) ?
The solution to 1/2 ln|3+e^8|-ln(2) is ln(((3+e^8)^{1/2})/2)