Logarithmic and Exponential Equations

The video tutorial covers exponential and logarithmic equations, focusing on solving them using key strategies like the one-to-one and inverse properties. It includes various examples, from basic to complex, demonstrating how to apply these strategies effectively. The tutorial also addresses exponentiating to solve logarithmic equations and concludes with a real-world story problem involving continuous compounding interest.

What is the one-to-one property for exponential equations?

• If a^x = a^y, then x must equal y.

• If a^x = a^y, then x must be greater than y.

• If a^x = a^y, then x must be less than y.

• If a^x = a^y, then x and y are unrelated.

How can you solve the equation 2^x = 512?

• Rewrite 512 as 2^9 and set x = 9.

• Rewrite 512 as 2^8 and set x = 8.

• Rewrite 512 as 2^10 and set x = 10.

• Rewrite 512 as 2^7 and set x = 7.

What is the solution to the equation ln(5) - ln(x) = 0?

• x = 0

• x = 10

• x = 1

• x = 5

How do you solve the equation 1/5^x = 125?

• Rewrite 1/5 as 5^-1 and 125 as 5^4, then set -x = 4.

• Rewrite 1/5 as 5^-2 and 125 as 5^3, then set -x = 3.

• Rewrite 1/5 as 5^-1 and 125 as 5^2, then set -x = 2.

• Rewrite 1/5 as 5^-1 and 125 as 5^3, then set -x = 3.

What is the inverse property for logarithms?

• log base a of a^x equals x.

• log base a of a^x equals 0.

• log base a of a^x equals a.

• log base a of a^x equals 1.

How do you solve the equation e^x = 13?

• Take the natural log of both sides to get x = ln(14).

• Take the natural log of both sides to get x = ln(12).

• Take the natural log of both sides to get x = ln(15).

• Take the natural log of both sides to get x = ln(13).

What is the solution to the equation ln(x) = -8?

• x = e^7

• x = e^8

• x = e^-8

• x = e^-7

How do you solve the equation log base 10 of x = -2?

• Rewrite as 10^(-2) = x, so x = 0.01.

• Rewrite as 10^(-2) = x, so x = 10.

• Rewrite as 10^(-2) = x, so x = 100.

• Rewrite as 10^(-2) = x, so x = 1/100.

What is the first step in solving the equation 4 * 3^x = 64?

• Multiply both sides by 4.

• Subtract 4 from both sides.

• Add 4 to both sides.

• Divide both sides by 4.

How do you solve the equation 3e^x = 2?

• Multiply both sides by 3e^x.

• Divide both sides by 3e^x.

• Add 3e^x to both sides and subtract 2.

• Subtract 3e^x from both sides and add 2.