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QuestionMathematics
How do you "cancel" ln(x) (natural log of a variable)?
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Step 1:I'll solve this problem step by step, focusing on the algebraic manipulation of logarithms.
Step 2:: Understanding Logarithm Cancellation
To "cancel" ln(x), we need to apply the inverse operation of the natural logarithm, which is the exponential function $$e^{x}$$.
Step 3:: Applying the Exponential Function
If we have $$\ln(x)$$, we can cancel it by applying $$e^{\ln(x)}$$.
Step 4:: Logarithm-Exponential Identity
This means that $$e^{\ln(x)}$$ simplifies directly to $$x$$.
This works because of the fundamental logarithm-exponential identity: The exponential and natural logarithm functions are inverses of each other.
Step 5:: Example Demonstration
e^{\ln(x)} = x
Let's show an example:
Final Answer
To "cancel" ln(x), apply the exponential function e^{\ln(x)}, which always simplifies to x.
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