Evaluate Logarithms With Natural Base Worksheet

Algebra 2
Logarithms

Total questions - 0

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How Will This Worksheet on "Evaluate Logarithms with Natural Base" Benefit Your Student's Learning?

  • Helps with calculus, like finding slopes and areas under curves using exponential and logarithmic functions.
  • Used in science and economics to predict how things grow or decrease quickly.
  • Improves problem-solving by dealing with equations that have logarithms and exponents.
  • Gives exact ways to figure out how things change and transform.
  • Useful in finance for figuring out how investments grow over time.

How to Evaluate Logarithms with Natural Base?

  • The natural logarithm \( \ln x \) with base \( e \) is the exponent to which \( e \) must be raised to equal \( x \).
  • \( \ln x \) and \( e^x \) are inverse functions, meaning \( \ln(e^x) = x \) and \( e^{\ln x} = x \).
  • To evaluate \( \ln(e^3) \), recognize that \( \ln(e^3) = 3 \) because \( e \) raised to the power of \( 3 \) equals \( e^3 \).

Solved Example

Q. Evaluate. Write your answer as a whole number, proper fraction, or improper fraction in simplest form.\newlineln(e)10=\frac{\ln (e)}{10} = ______
Solution:
  1. Evaluate expression: We need to evaluate the expression ln(e)10\frac{\ln(e)}{10}. The natural logarithm of ee, denoted as ln(e)\ln (e), is a special value in mathematics. The natural logarithm function is the inverse of the exponential function, so ln(e)\ln(e) is asking for the power to which ee must be raised to get ee. Since ee to the power of 11 is ee, ln(e)\ln(e) equals 11.
  2. Substitute ln(e)\ln(e) value: Now that we know ln(e)\ln(e) equals 11, we can substitute this value into our original expression.\newline So, ln(e)10\frac{\ln(e)}{10} becomes 110\frac{1}{10}.
  3. Simplify fraction: The fraction 110\frac{1}{10} is already in its simplest form. There is no common factor between the numerator and the denominator other than 11, so it cannot be simplified further.
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About Worksheet

Algebra 2
Logarithms

Evaluating logarithms with the natural base \( e \) involves finding the exponent that \( e \) must be raised to equal a given number. The natural logarithm, denoted as \( \ln x \), is the inverse of the exponential function \( e^x \). This means \( \ln(e^x) = x \) and \( e^{\ln x} = x \). For example, \( \ln(e^3) = 3 \) because \( e \) raised to the power of \( 3 \) equals \( e^3 \). Use this worksheet to enhance your understanding on logarithms.

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