Question

How do you express y in terms of x in an equation of $\ln y=x+2$?

Answer 1

Hint: Raise both the sides by the power of ‘e’ to eliminate the logarithm part from the equation. Then keep the terms containing ‘y’ on the left side of the equation and the ‘x’ terms and the constant terms on the right side to express ‘y’ in terms of ‘x’.

Complete step by step answer:
The equation we have, $\ln y=x+2$
To express ‘y’ in terms of ‘x’, first we need to eliminate the logarithm part.
From the exponential principle, we know that ${{e}^{\ln a}}=a$
Raising both the sides of the equation by ‘e’, we get
$\Rightarrow {{e}^{\ln y}}={{e}^{\left( x+2 \right)}}$
Cancelling out ‘e’ to the power ln part from the left side of the equation, we get
$\Rightarrow y={{e}^{\left( x+2 \right)}}$
Since, the containing ‘y’ is already on the left side of the equation and the remaining terms are on the right side
Hence, this is the required solution of the given question.

Note: As we know the general base of $\ln $ is ‘e’ so by raising both the sides of the equation by ‘e’ we can cancel out the ‘e’ to the power $\ln $ part to eliminate the logarithm part from the equation.