4.09 Log and Exp

What does a logarithm 'undo' in an equation?

• A multiplication

• An exponent (power)

• A subtraction

• A division

Which base of logarithms is used when the base term is a number?

• Natural log

• Logarithm to the base 10

• Logarithm to the base e

• Logarithm to the base 2

What is used when the base term is e?

• Logarithm to the base 10

• Natural log

• Square root

• Logarithm to the base 2

What is the first step in solving equations using logarithms?

• Divide through by a coefficient

• Factorise the left-hand side

• Take logs of both sides

• Expand the brackets

Which law allows you to bring down the powers when using logarithms?

• The law of exponents

• The law of multiplication

• The log law

• The law of division

What do you do after expanding the brackets when solving logarithmic equations?

• Bring all terms involving x over to one side

• Multiply through by the leading coefficient

• Subtract the constant term

• Take the square root of both sides

What is the final step in solving logarithmic equations?

• Graph the equation

• Simplify the equation

• Take the natural log of both sides

• Evaluate with a calculator

When solving with logarithms, what do you do with the x terms in the equation?

• Convert them to exponential form

• Multiply them by the base

• Cancel them out

• Isolate them on one side

What is the purpose of taking the natural log in solving equations?

• To simplify multiplication

• To eliminate the base e

• To isolate the variable

• To add constants

Which of the following is a common base of logarithms mentioned?

• Base 2

• Base 7

• Base 10

• Base 5