Solving Exponential Equations with Logarithms

This video tutorial explains how to solve exponential equations by applying the properties of logarithms. It covers the process of taking the logarithm of both sides of an equation when a common base cannot be found, and demonstrates this method with two examples: solving 6^x = 42 and 7^x = 20. The tutorial emphasizes the use of the power property of logarithms to bring the exponent down and solve for the variable.

What is the first step in solving an exponential equation when you cannot find a common base?

• Multiply both sides by the base

• Take the logarithm of both sides

• Add the exponents

• Subtract the exponents

In the equation 6^x = 42, what is the next step after taking the logarithm of both sides?

• Apply the power property of logarithms

• Subtract the logarithms

• Add the logarithms

• Multiply the logarithms

After applying the power property of logarithms to 6^x = 42, what is the resulting equation?

• log(6) / x = log(42)

• x + log(6) = log(42)

• log(6) * log(x) = log(42)

• x * log(6) = log(42)

What is the value of x when solving the equation 6^x = 42?

• 2.08

• 2.86

• 3.14

• 1.54

In the equation 7^x = 20, what is the first step after taking the logarithm of both sides?

• Apply the power property of logarithms

• Subtract the logarithms

• Multiply the logarithms

• Add the logarithms

After applying the power property of logarithms to 7^x = 20, what is the resulting equation?

• x + log(7) = log(20)

• log(7) * log(x) = log(20)

• log(7) / x = log(20)

• x * log(7) = log(20)

What is the value of x when solving the equation 7^x = 20?

• 2.08

• 2.86

• 1.54

• 3.14

What should you do if you cannot find a common base for the values in an exponential equation?

• Take the logarithm of both sides

• Add the exponents

• Subtract the exponents

• Multiply both sides by the base

What property of logarithms allows you to bring the exponent down in front?

• Product property

• Quotient property

• Power property

• Change of base property

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

• Add the logarithms

• Divide by the logarithm of the base

• Multiply the logarithms

• Subtract the logarithms