Where does logarithmic equations come from

The video tutorial explains how to find the inverse of a function by swapping the input and output variables and solving for the new output. It covers various inverse operations and introduces logarithmic form for equations with exponents. The tutorial emphasizes understanding the relationship between exponential and logarithmic forms, providing a clear explanation of how to interpret and use logarithms in solving equations.

What is the first step in finding the inverse of a function?

• Divide by the coefficient of X

• Multiply both sides by 2

• Swap the variables X and Y

• Add 5 to both sides

Which operation would you use to isolate Y if it is being multiplied by a number?

• Divide both sides by the number

• Multiply both sides by the number

• Add the number to both sides

• Subtract the number from both sides

Which of the following is NOT a step in solving for Y in an equation?

• Using inverse operations

• Swapping X and Y

• Adding the same number to both sides

• Ignoring the exponent

What is the purpose of using logarithmic form in equations?

• To simplify addition

• To solve equations with Y in the exponent

• To convert fractions to decimals

• To eliminate square roots

In logarithmic form, what does 'log base a of X equals Y' mean?

• a raised to the power of Y equals X

• X raised to the power of a equals Y

• Y raised to the power of a equals X

• a raised to the power of X equals Y

How do you express an exponential equation in logarithmic form?

• By adding the base to both sides

• By subtracting the exponent from both sides

• By rewriting it as 'log base a of X equals Y'

• By multiplying both sides by the base

What does the logarithmic form help to determine in an equation?

• The sum of two numbers

• The product of two numbers

• The power to which a base must be raised to get a number

• The difference between two numbers