Exploring Adding and Subtracting Rational Expressions

This video tutorial covers solving exponential equations using logarithms. It begins with a review of solving equations using a common base and then introduces two methods for when a common base is not possible. Method one involves taking the log of both sides, while method two involves rewriting the equation in logarithmic form. The tutorial includes practice problems and solutions, demonstrating both methods and emphasizing the importance of choosing the method that works best for the learner.

What is the result of solving the equation 5^(n+10) = 25?

• n = -8

• n = 10

• n = 8

• n = -10

What is the value of 'a' when solving 9^(a+2) = 27^(4a-2)?

• a = -1

• a = 2

• a = 1

• a = 0

How do you solve 2^(x) = 61 using logarithms?

• Multiply both sides by log(2)

• Find a common base for 2 and 61

• Use the change of base formula

• Divide both sides by 61

What is the correct expression for solving 2 to the x power equals 61 in logarithmic form?

• x log 2 equals 61

• log base 2 of 61 equals x

• 2 log x equals 61

• log base 61 of 2 equals x

When solving 8^(m-7) = 92, what is the first step using logarithms?

• Subtract 7 from both sides

• Divide both sides by 8

• Take the log of both sides

• Add 7 to both sides

What is the result of solving the equation 4^(3w) = 8 using logarithms?

• w = -0.5

• w = 0.5

• w = 1.5

• w = 2

How do you solve 5^(3k-3) = 4 using logarithms?

• Multiply both sides by 3

• Find a common base for 5 and 4

• Subtract 3 from both sides first

• Take the log of both sides and use the power rule

What is the value of 'p' when solving -2 * 5^(p+7) = -63 using logarithms?

• p = 7

• p = -2.2091

• p = -7

• p = 2.2091

What is the final step in solving for 'n' in the equation 3 * 8^(3-7n) + 10 = 94 using logarithms?

• Multiply both sides by 3

• Take the log of both sides

• Add 10 to both sides

• Divide both sides by -7

What is the correct step when you encounter a negative value inside a logarithm?

• Divide by -1

• Take the absolute value

• Multiply by -1

• The equation has no solution