Convert Logarithmic Equation In Exponential Form Worksheet

Algebra 2
Logarithms

Total questions - 0

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

  • Converting logarithmic equations to exponential form helps students discover unknowns more easily.
  • Understanding both forms enables students to see the link between logarithms and exponents.
  • Practicing these conversions improves students' skills in handling algebraic equations.
  • Converting equations provides another method for solving math problems.
  • Knowing how to convert these equations is essential for calculus and higher-level math courses.

How to Convert Logarithmic Equation in Exponential Form?

  • Identify the base, argument, and result in the logarithmic equation.
  • Note that the base is the number after "log," the argument is the number inside the logarithm, and the result is what the logarithm equals.
  • Convert \(\log_a(b) = c\) to exponential form \(a^c = b\).

Solved Example

Q. Write the logarithmic equation in exponential form.\newlinelog7373=3\log_7 373 = 3
Solution:
  1. Identify Values: log2(8)=3\log_2(8) = 3\newlineIdentify bb, xx, and yy.\newlineCompare log2(8)=3\log_2(8) = 3 with logb(x)=y\log_b(x) = y.\newlineb=2b = 2\newlinex=8x = 8\newliney=3y = 3
  2. Convert to Exponential: \newlinelog2(8)=3\log_2(8) = 3\newlineConvert the logarithmic equation to exponential equation.\newlineSubstitute b=2b = 2, x=8x = 8, and y=3y = 3 in by=xb^y = x.\newlineExponential equation: 23=82^3 = 8
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About Worksheet

Algebra 2
Logarithms

To convert a logarithmic equation to exponential form, identify the base, the argument, and the result. For a logarithmic equation \(\log_a(b) = c\), convert it to exponential form as \(a^c = b\). This conversion shows that raising the base \(a\) to the exponent \(c\) equals the argument \(b\). This highlights the inverse relationship between logarithms and exponents. Use this worksheet to enhance your understanding of exponential and logarithmic functions.

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