Solving Exponential and Logarithmic Equations

The video tutorial covers solving exponential and logarithmic equations using key strategies like the one-to-one and inverse properties. It provides examples ranging from basic to complex equations, including quadratic forms and real-world applications. The tutorial emphasizes rewriting equations in different forms to apply these properties effectively.

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 less than y.

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

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

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

• Rewrite 512 as 2^9 and set x = 9.

• Rewrite 512 as 2^7 and set x = 7.

• Rewrite 512 as 2^8 and set x = 8.

• Rewrite 512 as 2^10 and set x = 10.

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

• x = -5

• x = 1

• x = 0

• 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 0.

• log base a of a^x equals 1.

• log base a of a^x equals a.

• log base a of a^x equals x.

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

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

• 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(14).

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

• x = -e^-8

• x = e^-8

• x = e^8

• x = -e^8

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

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

• Rewrite as 10^(-2) = x, so x = 100.

• Rewrite as 10^(-2) = x, so x = 10.

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

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

• Subtract 4 from both sides to get 3^x = 60.

• Multiply both sides by 4 to get 3^x = 256.

• Divide both sides by 4 to get 3^x = 16.

• Add 4 to both sides to get 3^x = 68.

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

• Multiply both sides by 3 and add 2.

• Divide both sides by 3 and subtract 2.

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

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