Convert Exponential Equation In Logarithmic Form Worksheet

Algebra 2
Logarithms

Total questions - 0

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How Will This Worksheet on "Convert Exponential Equation in Logarithmic Form" Benefit Your Student's Learning?

  • Converting exponential equations to logarithmic form simplifies solving for unknown exponents, making it easier for students to handle complex equations.
  • Understanding both exponential and logarithmic forms deepens students' comprehension of the relationship between these concepts.
  • This conversion offers alternative problem-solving strategies, enhancing students’ mathematical toolkit.
  • Real-world situations, such as population growth and substance decay, use these skills, making this knowledge practical.
  • Logarithms are essential in calculus, particularly for working with exponential functions, critical for advanced math courses.

How to Convert Exponential Equation in Logarithmic Form?

  • Identify the base, exponent, and result in the exponential equation.
  • Note that the base is the number raised to a power, the exponent is the power, and the result is the operation's outcome.
  • Convert the exponential form \(a^b = c\) to the logarithmic form \(\log_a(c) = b\).

Solved Example

Q. Convert the exponential equation in logarithmic form.\newline93=7299^3 = 729
Solution:
  1. Exponential and Logarithmic Forms: Understand the relationship between exponential and logarithmic forms.\newlineAn exponential equation of the form by=xb^y = x can be rewritten in logarithmic form as logbx=y\log_b x = y, where bb is the base, yy is the exponent, and xx is the result.
  2. Components of Exponential Equation: Identify the components of the exponential equation.\newlineIn the equation 93=7299^3 = 729, the base (b)(b) is 99, the exponent (y)(y) is 33, and the result (x)(x) is 729729.
  3. Conversion to Logarithmic Form: Convert the exponential equation to logarithmic form. \newlineby=xb^y = x can be rewritten as logbx=y\log_b x = y. \newline 93=7299^3 = 729 can be rewritten as log9729=3\log_9 729 = 3.
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About Worksheet

Algebra 2
Logarithms

To convert an exponential equation to logarithmic form, identify the base, the exponent, and the result. Given an exponential equation of the form \(a^b = c\), rewrite it in logarithmic form as \(\log_a(c) = b\). This means that the logarithm of \(c\) with base \(a\) is equal to the exponent \(b\). Logarithms are the inverse operations of exponentiation, expressing the power to which the base must be raised to obtain the given number.

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