Solve Exponential Equations Using Log Worksheet

Algebra 2
Exponential Functions

Total questions - 6

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How Will This Worksheet on "Solve Exponential Equations Using Log" Benefit Your Student's Learning?

  • Using logs makes exponential equations simpler and easier to clear up.
  • Working with logs helps students understand how logarithms function.
  • This technique improves algebra talents through practicing exponent and log regulations.
  • Solving these equations boosts logical questioning and careful analysis.
  • Students learn to break down complex problems into simpler steps.
  • Successfully solving these equations builds confidence with difficult math standards.

How to Solve Exponential Equations Using Log?

  • Start with an equation in the form \( a^x = b \), where \( a \) and \( b \) are constants.
  • Take the logarithm of both sides of the equation using a common logarithm (log base `10`) or natural logarithm `(`log base `e)`: \( \log(a^x) = \log(b) \).
  • Utilize the property \( \log(a^x) = x \cdot \log(a) \) to move the exponent in front: \( x \cdot \log(a) = \log(b) \).
  • Isolate the variable \( x \) by dividing both sides by \( \log(a) \): `x = \frac{\log(b)}{\log(a)}`.

Solved Example

Q. Solve. Round your answer to the nearest thousandth.\newline7x=27^x = 2\newlinex=x = __
Solution:
  1. Write Equation: Write down the equation.\newlineWe are given the equation 7x=27^x = 2. We need to solve for xx.
  2. Apply Logarithm: Apply the logarithm to both sides of the equation.\newlineTo solve for xx, we can use logarithms. Applying the natural logarithm (ln\ln) to both sides gives us ln(7x)=ln(2)\ln(7^x) = \ln(2).
  3. Use Power Property: Use the power property of logarithms. The power property of logarithms states that ln(ab)=bln(a)\ln(a^b) = b\cdot\ln(a). We apply this property to simplify the left side of the equation: xln(7)=ln(2)x\cdot\ln(7) = \ln(2).
  4. Isolate x: Isolate xx.\newlineTo solve for xx, we divide both sides of the equation by ln(7)\ln(7): x=ln(2)ln(7)x = \frac{\ln(2)}{\ln(7)}.
  5. Calculate Value: Calculate the value of xx. Using a calculator, we find the values of ln(2)\ln(2) and ln(7)\ln(7) and then divide them to find xx. x=ln(2)ln(7)0.693147181.945910150.356207187x = \frac{\ln(2)}{\ln(7)} \approx \frac{0.69314718}{1.94591015} \approx 0.356207187
  6. Round Answer: Round the answer to the nearest thousandth.\newlineRounding the value of xx to the nearest thousandth gives us x0.356x \approx 0.356.
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About Worksheet

Algebra 2
Exponential Functions

To solve exponential equations using logs, take the logarithm of both sides to bring the exponents down. This transforms the equation into a linear form that can be easily solved for the variable. Solving exponential equations using a log worksheet provides practice problems, and solving exponential equations using logarithms pdf offers a comprehensive guide and examples for mastering this method.

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