Solving Exponential Equations with Logarithms

This video tutorial focuses on solving exponential equations in quadratic form. It begins with an introduction to the topic, followed by detailed solutions to three example problems. The instructor uses substitution and natural logarithms to solve the equations, demonstrating each step clearly. The video also explores an alternative method for solving exponential equations, emphasizing the properties of exponential functions and natural logs. Key concepts include substitution, factoring, and the use of natural logarithms to solve for variables.

What substitution is used to simplify the equation e^(2x) - 5e^x + 6 = 0?

• a = x^2

• a = e^(2x)

• a = 2e^x

• a = e^x

Which pair of numbers multiplies to 6 and adds to -5?

• 2 and 3

• -2 and -3

• 1 and 6

• -1 and -6

What is the value of x when e^x = 2?

• ln(2)/2

• ln(2)

• ln(4)

• 2ln(e)

What does e^x equal when a = 7 in the equation a^2 - 3a - 28 = 0?

• 2

• 7

• -4

• 3

Why can't e^x be equal to -4?

• e^x is always zero

• e^x is undefined

• e^x is always positive

• e^x can be any real number

What is the correct factorization of a^2 - 14a + 48?

• a - 4 and a - 12

• a - 8 and a - 6

• a + 8 and a + 6

• a + 4 and a + 12

What is the value of x when e^(2x) = 8?

• ln(8)/2

• ln(8)

• 2ln(8)

• ln(4)

What is the equivalent expression for the square root of 8?

• 8^(1/2)

• 4^(1/2)

• 16^(1/2)

• 2^(1/2)

What is the value of x when e^(2x) = 6?

• ln(3)

• ln(6)/2

• ln(6)

• 2ln(6)

What is the natural logarithm of a square root equivalent to?

• 1/2 times the natural logarithm of the original number

• 2 times the natural logarithm of the original number

• The natural logarithm of twice the original number

• The natural logarithm of the original number divided by 2