Question

Evaluate \( \cosh (\log 4) \):

• A. \( \frac{8}{17} \)
• B. \( \frac{17}{8} \)
• C. \( 0 \)
• D. \( \frac{9}{8} \)

Hint:

For hyperbolic functions involving logarithms, use exponent properties: \( e^{\log a} = a \) and \( e^{-\log a} = \frac{1}{a} \).

Answer 1

The Correct Option is B

Step 1: Definition of hyperbolic cosine The formula for hyperbolic cosine is: \[ \cosh x = \frac{e^x + e^{-x}}{2}. \] Substituting \( x = \log 4 \): \[ \cosh (\log 4) = \frac{e^{\log 4} + e^{-\log 4}}{2}. \] Step 2: Evaluating exponential terms Since \( e^{\log 4} = 4 \) and \( e^{-\log 4} = \frac{1}{4} \), we get: \[ \cosh (\log 4) = \frac{4 + \frac{1}{4}}{2} = \frac{\frac{16}{4} + \frac{1}{4}}{2} = \frac{\frac{17}{4}}{2} = \frac{17}{8}. \]