Logarithms Review for Calculus

Logarithmic functions are the inverse of...

• Linear Functions

• Exponential Functions

• Quadratic Functions

• Polynomial Functions

Exponential functions are the inverse of...

• Linear Functions

• Polynomial Functions

• Quadratic Functions

• Logarithmic Functions

Which number(s) are the most common bases for logarithms?

• $1$

• $10$

• $e$

• $\pi$

Which logarithmic properties do you remember learning about in previous courses?

• Product Property

• Quotient Property

• Power Property

• Change of Base Property

Which of the following illustrates the Product Property of Logarithms?

•  $\log_3\left(x\right)+\log_3\left(y\right)=\log_3\left(x+y\right)$  

•  $\log_3\left(x\right)\cdot\log_3\left(y\right)=\log_3\left(xy\right)$  
  

•  $\log_3\left(x\right)+\log_3\left(y\right)=\log_3\left(xy\right)$  

•  $\log_3\left(x\right)\cdot\log_3\left(y\right)=\log_3\left(x+y\right)$  

Which of the following illustrates the Quotient Property of Logarithms?

•  $\log_4\left(x\right)-\log_4\left(y\right)=\log_4\left(x-y\right)$  

•  $\log_4\left(x\right)\div\log_4\left(y\right)=\log_4\left(\frac{x}{y}\right)$  
  

•  $\log_4\left(x\right)-\log_4\left(y\right)=\log_4\left(\frac{x}{y}\right)$  

•  $\log_4\left(x\right)\div\log_4\left(y\right)=\log_4\left(x-y\right)$  

Which of the following illustrates the Power Property of Logarithms?

• $\log_5\left(m^n\right)=n+\log_5\left(m\right)$

• $\log_5\left(m^n\right)=n\cdot\log_5\left(m\right)$

• $\log_5\left(m^n\right)=\log_5\left(n\cdot m\right)$
  

• $\log_5\left(m^n\right)=\log_{5n}\left(m\right)$

Which of the following illustrates the Change of Base Property of Logarithms? (select all that apply)

• $\log_8\left(p\right)=\frac{\ln\left(p\right)}{\ln\left(8\right)}$

• $\log_8\left(p\right)=\ln\left(p\right)\cdot\ln\left(8\right)$

• $\log_8\left(p\right)=\ln\left(p\right)+\ln\left(8\right)$

• $\log_8\left(p\right)=\frac{\log\left(p\right)}{\log\left(8\right)}$

• $\log_8\left(p\right)=\frac{1}{\ln\left(8\right)}\cdot\ln\left(p\right)$

Evaluate (without using your GDC): $\log_525$  

(a)  

Simplify: $\ln\left(e^{4x}\right)$  

(a)