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Exercise

$y=\ln\left(\sqrt{1+e^x}-1\right)-\ln\left(\sqrt{1+e^x}+1\right)$

Step-by-step Solution

1

The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$

$y=\ln\left(\frac{\sqrt{1+e^x}-1}{\sqrt{1+e^x}+1}\right)$

Final answer to the exercise

$y=\ln\left(\frac{\sqrt{1+e^x}-1}{\sqrt{1+e^x}+1}\right)$

Try other ways to solve this exercise

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  • Differential
  • Find the derivative
  • Find the integral
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
  • Simplify
  • Find the integral
  • Find the derivative
  • Factor
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Similar Questions Solved

$derivdef\left(\ln\left(x\right)\right)$

Main Topic: Properties of Logarithms

They are properties that can help us simplify expressions with logarithms.

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