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How do you solve ln y = 2x + 4?

Last updated date: 24th Jul 2024
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Hint:In the given question, we have been asked to solve ln y = 2x + 4. In order to solve the question, first we need to cancel out the log function from the equation. To get rid of a logarithm function from an equation, we need to raise both sides to the same exponent as the base of the logarithms. In the given question to eliminate or cancel out the natural log, we need to raise both sides by the power of ‘e’, then simplify the given equation. In this way we get our required solution.

Complete step by step solution:
We have given that,
\[\Rightarrow \ln y=2x+4\]
To eliminate or cancelling out the natural log, we need to raising both sides by the power of ‘e’,
We get the equation,
\[\Rightarrow {{e}^{\ln \left( y \right)}}={{e}^{2x+4}}\]
\[\Rightarrow y={{e}^{2x+4}}\]
Therefore, the value of \[y={{e}^{2x+4}}\] is the required solution.

Note: In the given question, we need to find the value of ‘x’. To solve these types of questions, we used the basic formulas of logarithm. Students should always require to keep in mind all the formulae for solving the question easily. After applying log formulae to the equation, we need to solve the equation in the way we solve general linear equations. Students should always remember that natural log and the exponential functions are the inverse of each other, which means that if we raise the exponential function by the natural log of x, then only we would be able to find the value of ‘x’.