Exponential Equations and Functions

The video tutorial by Houston Map Prep introduces solving exponential equations with like bases. It covers setting exponents equal when bases are the same, recognizing numbers as powers of a base, and using properties of exponents. The tutorial also explains changing bases to a common base and solving quadratic equations derived from exponential equations.

What is the first step in solving exponential equations with like bases?

• Multiply the exponents

• Set the exponents equal to each other

• Subtract the exponents

• Add the exponents

Why do exponential functions pass the horizontal line test?

• They are always increasing

• They are one-to-one functions

• They are always decreasing

• They have a constant rate of change

When solving 2^(x+3) = 2^(2x-1), what equation do you solve?

• 2x + 3 = 2x - 1

• x + 3 = 2x - 1

• x + 3 = x - 1

• 2x + 3 = x - 1

How can you express 49 as a power of 7?

• 7^1

• 7^3

• 7^4

• 7^2

What is the solution to the equation 5^(x+1) = 25?

• x = 0

• x = 1

• x = 2

• x = 3

How do you express 1/9 as a power of 3?

• 3^-1

• 3^2

• 3^-2

• 3^1

What is the base conversion for 6^x = 36^(x-1)?

• Convert 36 to 6^3

• Convert 6 to 36^1

• Convert 36 to 6^2

• Convert 6 to 36^2

How do you solve 4^x = 8^(x+1) using a common base?

• Convert both to base 8

• Convert both to base 2

• Convert both to base 4

• Convert both to base 16

What is the solution to the equation 27^(x-1) = 9^(x+5)?

• x = 4

• x = -3

• x = 13

• x = 0

How do you solve x^2 = 4x using factoring?

• Divide by x

• Use the quadratic formula

• Subtract 4x and factor

• Add 4x and factor