calculate cosh(ln(2))

Let's evaluate:

\cosh (\ln (2))

Replace cosh by its definition:

\cosh (x) = \frac{e^{x} + e^{- x}}{2}

ⅰ

\cosh (\ln (2))

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

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

ⓘ For real

x

\ln (\exp (x)) = x

; wherever

\ln (x)

is defined,

\exp (\ln (x)) = x

e^{\ln (2)}

2

e^{- \ln (2)}

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

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

ⓘ For real

x

\ln (\exp (x)) = x

; wherever

\ln (x)

is defined,

\exp (\ln (x)) = x

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

\frac{1}{2}

■To add fractions, put them over the same denominator, then add the numerators:

2 + \frac{1}{2}

\frac{2 \times 2 + 1}{2}

\frac{\frac{2 \times 2 + 1}{2}}{2}

ⓘ Multiplications are done before additions and subtractions:

2 \times 2

4

\frac{\frac{4 + 1}{2}}{2}

ⓘ The numerator and the denominator are computed before the division:

4 + 1

5

\frac{\frac{5}{2}}{2}

ⓘ Dividing a fraction by

2

is multiplying its denominator by

2

\frac{\frac{5}{2}}{2}

\frac{5}{2 \times 2}

\frac{5}{2 \times 2}

ⅰ

2 \times 2

4

▶Result:

\frac{5}{4}

The numeric value of:

\frac{5}{4}

equals:

▷

1.25

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