Adding and Subtracting Rational Expressions

What is the first step in solving exponential equations using logarithms when a common base is not applicable?

• Isolate the exponential expression

• Take the logarithm of both sides

• Check for extraneous solutions

• Expand the logarithms using the power rule

What rule allows you to move the exponent in front of the logarithm?

• Chain rule

• Power rule

• Quotient rule

• Product rule

Which logarithmic property is used to simplify 'log(AB)'?

• Power rule

• Product rule

• Quotient rule

• None of the above

After applying the power rule, what is the next step in solving for x in logarithmic equations?

• Divide both sides by the logarithm of the base

• Add the exponent to both sides

• Subtract the base from both sides

• Multiply both sides by the base

What does 'Ln' represent in logarithmic equations?

• Natural logarithm

• Binary logarithm

• Logarithm base 10

• Common logarithm

What is the result of 'Ln(e)'?

• Undefined

• 1

• 0

• e

In solving complex logarithmic equations, what must you do after distributing the logs?

• Combine like terms

• Factor out the variable x

• Apply the quotient rule

• Isolate the logarithmic terms

How do you solve for x when both sides of the equation are logged with different bases?

• Divide the logs

• Subtract the logs

• Factor the logs

• Add the logs

When solving 'log(base 2) of 32 = x', what is the value of x?

• 5

• 4

• 2

• 8

What common error must be avoided when entering logarithmic calculations into a calculator?

• Ignoring the power rule

• All of the above

• Forgetting to close parentheses

• Using the wrong logarithmic base