Solving Exponential and Logarithmic Equations

The video tutorial explains how to solve exponential equations using logarithms. It covers two examples: solving 7^(4x+1) = 128 and e^(2x-5) = 61. The process involves isolating the exponential part, applying logarithms, and using properties of logarithms to solve for x. The tutorial demonstrates the use of natural logs and calculators for decimal approximations, ensuring solutions are verified.

What is the first step in solving an exponential equation using logarithms?

• Subtract a constant from both sides

• Add a constant to both sides

• Isolate the exponential part

• Multiply both sides by a constant

In the equation 7^(4x + 1) = 128, what logarithm is used to solve for x?

• Base 10 logarithm

• Binary logarithm

• Common logarithm

• Natural logarithm

What property of logarithms allows us to move the exponent to the front?

• Product property

• Quotient property

• Change of base property

• Power property

After applying the power property, what is the next step in solving for x in the equation 7^(4x + 1) = 128?

• Subtract natural log 7 from both sides

• Add natural log 7 to both sides

• Divide both sides by 4

• Multiply both sides by 4

What is the approximate value of x in the equation 7^(4x + 1) = 128?

• 0.5678

• 0.3734

• 0.9876

• 0.1234

In the equation e^(2x - 5) = 61, why is the natural logarithm preferred?

• It matches the base of the exponential

• It simplifies the equation

• It is easier to calculate

• It is more accurate

What is the value of natural log e?

• 1

• 0

• 10

• e

What is the next step after simplifying 2x - 5 = natural log 61?

• Divide both sides by 2

• Multiply both sides by 2

• Add 5 to both sides

• Subtract 5 from both sides

What is the approximate value of x in the equation e^(2x - 5) = 61?

• 5.6789

• 4.5554

• 6.7890

• 3.1415

How can you verify the solution for x in the equation e^(2x - 5) = 61?

• By checking if e raised to the calculated power equals 61

• By adding 5 to the calculated x

• By multiplying the calculated x by 2

• By subtracting 5 from the calculated x