Evaluate \( \cosh (\log 4) \):
Show Hint
- \( \frac{8}{17} \)
- \( \frac{17}{8} \)
- \( 0 \)
- \( \frac{9}{8} \)
The Correct Option is B
Solution and Explanation
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: \[ \cosh (\log 4) = \frac{4 + \frac{1}{4}}{2} = \frac{\frac{16}{4} + \frac{1}{4}}{2} = \frac{\frac{17}{4}}{2} = \frac{17}{8}. \]
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