Exponential and Linear Equations

The video tutorial explains how to solve exponential equations with fractions. It covers two equations, demonstrating the importance of having the same base for solving. The first equation is solved by expressing numbers as powers of their bases, leading to the solution x = 3. The second equation involves rewriting terms with a common base and solving the resulting linear equation, yielding x = -7. The tutorial concludes with a summary of the methods used.

What is the first step in solving exponential equations with fractions?

• Convert all terms to decimals

• Ensure the bases are the same

• Add all exponents together

• Multiply all terms by the denominator

In the equation 2 * 3^x = 8 * 27, what is the base of 8?

• 4

• 2

• 3

• 5

What is the value of x in the equation 2 * 3^x = 8 * 27?

• 1

• 2

• 3

• 4

What is the base of 4 in the second equation?

• 5

• 4

• 3

• 2

How can 8 be expressed in terms of base 2?

• 2^5

• 2^4

• 2^3

• 2^2

What is the expression for 1/4 in terms of base 2?

• 1/2^2

• 1/2^3

• 1/2^5

• 1/2^4

What is the expression for 1/8 in terms of base 2?

• 1/2^2

• 1/2^3

• 1/2^4

• 1/2^5

What is the base used for rewriting the second equation?

• 1/2

• 1/3

• 1/4

• 1/5

What is the expression for 1/2 in terms of base 2?

• 2^-2

• 2^-3

• 2^-4

• 2^-1

What is the expression for 1/2^3 in terms of base 2?

• 2^-1

• 2^-2

• 2^-3

• 2^-4