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Multiple Choice
Which operation can be used to eliminate a natural logarithm, such as , from an equation?
A
Take the square root of both sides
B
Multiply both sides by
C
Exponentiate both sides using base
D
Differentiate both sides
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Verified step by step guidance
1
Step 1: Understand the natural logarithm function ln(x). The natural logarithm is the inverse of the exponential function with base e. This means that if y = ln(x), then x = e^y.
Step 2: To eliminate a natural logarithm, you need to apply the inverse operation. The inverse operation of ln(x) is exponentiation with base e.
Step 3: If you have an equation involving ln(x), such as ln(x) = y, you can exponentiate both sides using base e to eliminate the logarithm. This transforms the equation into x = e^y.
Step 4: Note that exponentiating both sides using base e is a valid mathematical operation because it preserves the equality of the equation.
Step 5: Avoid other operations like taking the square root, multiplying by e, or differentiating, as they do not eliminate the natural logarithm effectively. Exponentiation with base e is the correct approach.