Exponential Equations and Logarithms

Which method would you do to start solving the below exponential equation?

• Take Log, base 10, on the left hand side

• Take Log, base 3, on the left hand side

• Take Log, base e, on the both sides

• Help?!?

After taking logs on both sides of the previous equation, you get the below equation. What is the next step?

• Divide both sides by x

• Multiply both sides by Log(3)

• Distribute the Log(3) term

• Use the change of base formula to calculate Log3

• You didn't cover this, did you?

What happen to the exponential function as the value of x decreases without bound?

• The function increases without bound.

• The function approaches to infinitiy

• The function approaches to the line x =0

• The function approaches to the line y=0

Which of the following is NOT a strategy that is often used to solve logarithmic equations?

• Express the equation in exponential form and solve the resulting exponential equations.

• Simplify the expressions in the equation by using the laws of logarithms

• Represent the sums or differences of logs as simple logarithms.

• Square all logarithmic expressions and solve the resulting quadratic equation.

It is mainly used, but not limited to , earthquake intensity measurement, acidic measurement of solutions (pH value), sound intensity measurement and expressing larger values.

• Rational function

• Exponential Function

• Logarithmic function

• Inverse Function

Convert log(x)=5 to exponential form

• ⁵=x

• ^x=5

• ⁵=10

• ⁵=x

Convert log(x)=y+2 to exponential form.

• 10^(y+2)=x

• 1^x=y+2

• 10^x=y+2

• x^(y+2)=10

log_x(64)=3

• x=8

• x=4

• x=3

• x=64

Convert log₁₂(x)=2 to exponential form.

• 12²=x

• 12^x=2

• x²=12

• 2^x=12

Find the inverse of f(x)=log₄(x+4)

• f^-1(x)=4^(x-4)

• f^-1(x)=4^x+4

• f^-1(x)=4^x-4

• f^-1(x)=4^x