Question

18. Express \( \operatorname{cosech}^{-1} x \) in terms of logarithm. Hence, solve the equation \[ \operatorname{cosech}^{-1} x+\ln x=\ln 3 \] 19. Solve the following equations simultaneously and give your answer in terms of logarithms. \[ \begin{array}{r} \cosh x-3 \sinh y=0 \\ 2 \sinh x+6 \cosh y=5 \end{array} \] 20. Find the positive root of the equation \[ \sin ^{-1} x+\cos ^{-1}(4 x)=\frac{\pi}{6} \]

          18. Express \( \operatorname{cosech}^{-1} x \) in terms of logarithm. Hence, solve the equation
\[
\operatorname{cosech}^{-1} x+\ln x=\ln 3
\]
19. Solve the following equations simultaneously and give your answer in terms of logarithms.
\[
\begin{array}{r}
\cosh x-3 \sinh y=0 \\
2 \sinh x+6 \cosh y=5
\end{array}
\]
20. Find the positive root of the equation
\[
\sin ^{-1} x+\cos ^{-1}(4 x)=\frac{\pi}{6}
\]

18. Express cosech^-1 x in terms of logarithm. Hence, solve the equation

cosech^-1 x+ln x=ln 3

19. Solve the following equations simultaneously and give your answer in terms of logarithms.

cosh x-3 sinh y=0

2 sinh x+6 cosh y=5

20. Find the positive root of the equation

sin ^-1 x+cos ^-1(4 x)=(π)/(6)

Added by Julian H.

Precalculus

Cynthia Young 2nd Edition

Chapter 3

Instant Answer

Solved by Expert Naresh Bagrecha

Step 1

The inverse hyperbolic cosecant function can be expressed as: \[ \operatorname{cosech}^{-1} x = \ln \left( \frac{1}{x} + \sqrt{\frac{1}{x^2} + 1} \right) \] Show more…

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18. Express \( \operatorname{cosech}^{-1} x \) in terms of logarithm. Hence, solve the equation \[ \operatorname{cosech}^{-1} x+\ln x=\ln 3 \] 19. Solve the following equations simultaneously and give your answer in terms of logarithms. \[ \begin{array}{r} \cosh x-3 \sinh y=0 \\ 2 \sinh x+6 \cosh y=5 \end{array} \] 20. Find the positive root of the equation \[ \sin ^{-1} x+\cos ^{-1}(4 x)=\frac{\pi}{6} \]