Solving Exponential Equations Without a Calculator

The video tutorial explains how to solve exponential equations using the one-to-one property. It begins with an introduction to the concept, followed by basic examples that do not require a calculator. The tutorial then covers handling negative exponents and fractions, applying exponent rules, and solving more complex equations with expressions as exponents. The instructor emphasizes the importance of rewriting bases to be the same and using the power rule to simplify equations.

What does the one-to-one property state?

• If a^x = a^y, then x = y

• If a^x = b^y, then x = y

• If a^x = b^y, then x = y + 1

• If a^x = a^y, then x = y + 1

If 4^x = 16, what is the value of x?

• x = 1

• x = 4

• x = 2

• x = 3

How can you rewrite 16 in the denominator using negative exponents?

• 8^-1

• 4^-2

• 2^-4

• 16^-1

What is the value of x if 2^-x = 32?

• x = -5

• x = 5

• x = -4

• x = 4

How do you handle fractions in exponential equations?

• Rewrite the fraction as a negative exponent

• Square the numerator and denominator

• Use the power rule

• All of the above

If 3^(2x) = 3^3, what is the value of x?

• x = 1/2

• x = 3/2

• x = 2/3

• x = 3

What is the value of x if 2^(2x-1) = 2^3?

• x = 3

• x = 2

• x = 1

• x = 4

If 5^(3(2x+1)) = 5^2, what is the value of x?

• x = -1/3

• x = 1/3

• x = -1/6

• x = 1/6

How do you solve exponential equations with different bases?

• Use the power rule

• All of the above

• Apply the distributive property

• Rewrite both sides with the same base

What is the value of x if 2^(3(x+1)) = 2^(4(x-1))?

• x = 5

• x = 7

• x = 3

• x = 1