How to solve exponential equations

The video tutorial explains how to solve exponential equations using two main methods: the one-to-one property and calculator methods involving logarithms. It begins with an introduction to exponential equations, followed by a detailed explanation of the one-to-one property, which is useful for equations with the same base. The tutorial then covers calculator methods, including taking the log of both sides and converting to logarithmic form. Finally, it discusses the change of base formula for cases where the one-to-one property cannot be applied.

What is the first step in solving an exponential equation like y = b^x?

• Divide both sides by b

• Multiply both sides by x

• Isolate the exponential term

• Add all terms to one side

What does the one-to-one property state?

• If b^x = b^y, then y = b

• If b^x = b^y, then x = y

• If b^x = b^y, then x = y + b

• If b^x = b^y, then x = b

How can you solve an exponential equation if the one-to-one property is not applicable?

• Multiply both sides by the base

• Use the quadratic formula

• Take the logarithm of both sides

• Add the exponents together

What is the purpose of taking the log of both sides in an exponential equation?

• To simplify the equation

• To convert to a quadratic form

• To isolate the exponent

• To eliminate the base

What does the change of base formula allow you to do?

• Simplify exponential expressions

• Solve equations without a calculator

• Find the exact value of an exponent

• Convert between different logarithmic bases

Which of the following is a correct application of the change of base formula?

• log base 2 of 10 over log base 7 of 2

• log base 7 of 2 over log base 10 of 2

• log base 2 of 7 over log base 2 of 10

• log base 10 of 7 over log base 10 of 2

When is it necessary to use the change of base formula?

• When the base is not a power of 2

• When the base cannot be expressed as a power of another number

• When the base is a negative number

• When the base is a fraction