Solving Exponential Equations with Equal Bases

The video tutorial explains how to solve exponential equations using the equal base method. It covers various examples, starting with simple cases where bases are already equal, and progresses to more complex scenarios involving rewriting bases, handling fractions, negative exponents, and radicals. The tutorial also touches on solving equations with the mathematical constant e. Each example is broken down step-by-step, demonstrating how to manipulate exponents and bases to find the solution.

What is the basic principle behind the equal base method for solving exponential equations?

• The exponents must be different.

• The exponents must be zero.

• The bases must be different.

• The bases must be equal.

In the equation 5^(3x - 6) = 125, what is the first step to solve for x?

• Subtract 3x from both sides.

• Add 6 to both sides.

• Divide both sides by 5.

• Rewrite 125 as 5^3.

What is the result of solving the equation 5^(3x) = 125?

• x = 1

• x = 4

• x = 3

• x = 2

When rewriting both bases as a smaller base, what common base can be used for 8 and 4?

• Base 2

• Base 3

• Base 10

• Base 5

In the equation 2^(3x + 6) = 2^(2x - 6), what is the next step after setting the exponents equal?

• Multiply both sides by 3.

• Divide both sides by 2.

• Subtract 2x from both sides.

• Add 6 to both sides.

In the equation 4^(2x) = 1/16, what exponent should be used to rewrite 1/16?

• 4^-3

• 4^3

• 4^-2

• 4^2

What is the value of x in the equation 4^(6x) = 64?

• x = 1/3

• x = 1/2

• x = 2/3

• x = 3/2

How do you handle a negative exponent when solving exponential equations?

• Move the base to the bottom.

• Move the base to the top.

• Add the exponent to both sides.

• Subtract the exponent from both sides.

How do you convert a cube root into a fractional exponent?

• Raise the base to the power of 1/3.

• Raise the base to the power of -3.

• Raise the base to the power of 3.

• Raise the base to the power of -1/3.

What is the value of x in the equation e^(x) = e^(-2x)?

• x = 0

• x = 1

• x = -1

• x = 2