Logarithmic and Exponential Functions

The video tutorial explains how to solve an exponential equation with different bases. It begins by breaking down the equation using exponent rules, rearranging terms, and simplifying. The instructor then applies logarithms to solve the equation and demonstrates the change of base formula for further simplification. The tutorial concludes with the final steps and simplification of the solution.

What is the first step in solving an exponential equation with different bases?

• Add the exponents

• Convert both sides to the same base

• Use logarithms immediately

• Multiply the bases

What rule is used to break down the expression 2^(x+3)?

• Product Rule

• Rule of Exponents

• Quotient Rule

• Power Rule

How can 2^(x+3) be expressed using the rule of exponents?

• 2^x + 2^3

• 2^(x/3)

• 2^(x*3)

• 2^x * 2^3

What is the value of 2^3?

• 6

• 8

• 9

• 12

What is the next step after simplifying the equation to 2^x * 8 = 3^x * 9?

• Subtract 9 from both sides

• Multiply both sides by 9

• Divide both sides by 8

• Add 8 to both sides

What operation is used to isolate the variable x in the equation 2^x/3^x = 9/8?

• Addition

• Subtraction

• Multiplication

• Division

Which logarithmic property is used to solve the equation 2^x = 3^x?

• Logarithm of a product

• Logarithm of a power

• Logarithm of a quotient

• Change of base formula

What is the base used in the logarithm to solve the equation 2^x = 3^x?

• 2/3

• 2

• 9/8

• 3

What is the change of base formula used for?

• Simplifying fractions

• Converting between different logarithm bases

• Solving quadratic equations

• Finding the derivative of a function

How is the expression ln(9/8) / ln(2/3) simplified?

• ln(9) * ln(8) / ln(2) * ln(3)

• ln(9) - ln(8) / ln(2) - ln(3)

• ln(9) + ln(8) / ln(2) + ln(3)

• ln(9) / ln(8) * ln(2) / ln(3)