Solving Exponential Equations

Mr. Ro introduces solving exponential equations, focusing on simplifying each side using exponent rules. He explains how to rewrite equations to have the same base and solve them by equating exponents. The video covers handling complex expressions and different bases, providing advanced examples and strategies for problem-solving.

What is the first step in solving an exponential equation?

• Set the exponents equal to each other.

• Ensure both sides have the same base.

• Multiply both sides by the same number.

• Use logarithms to simplify.

If you have 2^x = 2, what is the value of x?

• 0

• x cannot be determined

• 1

• 2

How do you solve 3^(x-4) = 3^(2x-3)?

• x = 0

• x = 1

• x = 2

• x = -1

What should you do if the bases are not the same, like in 2^x = 8?

• Divide both sides by 2.

• Add 8 to both sides.

• Rewrite 8 as 2^3.

• Use a calculator to find x.

In the equation 9^(2x) = 1/81, what is the rewritten form of 1/81?

• 3^4

• 3^-4

• 9^-2

• 9^2

What is a common mistake when solving exponential equations?

• Ignoring the exponents.

• Using the wrong base.

• Cancelling bases too early.

• Forgetting to simplify both sides.

How do you solve 16^(2y-1) = 4^(x-2) by rewriting the bases?

• Rewrite 4 as 16^0.5.

• Rewrite 16 as 2^4.

• Rewrite 4 as 2^2.

• Rewrite 16 as 4^2.

What is the solution to 4x + 4 = -2 when solving exponential equations?

• x = -1

• x = -2

• x = -3

• x = -4

When combining exponents, what should you do first?

• Subtract the exponents.

• Multiply the exponents.

• Add the exponents.

• Cancel the bases immediately.

In the equation 2^(1 + 2(3x-1)) = 2^(-3 + 2(2x+5)), what is the first step?

• Add 3 to both sides.

• Cancel the bases.

• Simplify the exponents.

• Multiply both sides by 2.