Solving Exponential Equations

This video tutorial covers solving exponential equations using logarithms, including graphical verification. It provides step-by-step solutions for various examples, demonstrating techniques like isolating exponential parts, applying logarithmic properties, and using graphing calculators for verification. The video aims to enhance understanding of solving exponential equations with practical examples and alternative methods.

What is the first step in solving exponential equations using logarithms?

• Multiply both sides by a constant

• Subtract a constant from both sides

• Isolate the exponential part

• Add a constant to both sides

Which logarithms are typically used when solving exponential equations?

• Binary and common logs

• Common and natural logs

• Natural and binary logs

• Decimal and binary logs

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CCSS.HSF.LE.A.4

In the first example, what is the approximate value of x when solving 7^x = 5?

• 1.05

• 0.75

• 0.95

• 0.83

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CCSS.HSF.LE.A.4

What alternative method can be used to solve 7^x = 5?

• Using the binomial theorem

• Using the change of base formula

• Using the quadratic formula

• Using the Pythagorean theorem

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CCSS.HSF.LE.A.4

In the second example, what is the approximate value of x when solving 2^x = 5?

• 1.32

• 2.32

• 3.32

• 4.32

What is the main challenge when graphically checking the solution for 2^x = 5?

• Finding the correct logarithm

• Adjusting the window to see the horizontal line

• Identifying the exponential part

• Calculating the exact value of x

In the third example, what is the approximate value of x when solving the equation with two exponential parts?

• 6.01

• 4.01

• 3.01

• 5.01

What is the final step in solving the complex exponential equation in the third example?

• Dividing by the sum of logs

• Subtracting the constants

• Multiplying by the base

• Adding the exponents

How can you verify the solution of an exponential equation graphically?

• By finding the y-intercept

• By checking the slope

• By calculating the area under the curve

• By finding the x-coordinate of the intersection point

What is the approximate value of x in the final example when solving the equation with two exponential parts?

• -9.1

• -8.1

• -11.1

• -10.1