Base e and ln function

Base e and ln function

Unit 9

Multiple Choice

Is the following graph an exponential growth or decay?

• Exponential Growth 

• Exponential Decay 

• None 

Multiple Choice

Simplify the following: 

 $x^4\cdot x^2$  

•  $x^2$  

•  $x^8$  

•  $x^6$  

•  $x^5$  

Multiple Choice

Simplify the following:

 $\frac{12x^3}{2x^2}$  

•  $6x^5$  

•  $6x$  

•  $10x^5$  

•  $10x$  

Multiple Choice

Identify the base and exponent for 2³ = 8.

• Base: 2

  Exponent: 3

• Base: 3

  Exponent: 2

• Base: 2

  Exponent: 8

• Base: 8

  Exponent: 3

Multiple Choice

Convert the exponential equation x³=8 to a logarithmic equation.

• $\log_x\left(3\right)=8$

• $\log_x\left(8\right)=3$

• $\log_8\left(x\right)=3$

• $\log_3\left(8\right)=x$

Multiple Choice

Evaluate and round to the nearest thousandth. 
 $\log_5100$ 

• 3.612

• 20

• 5.01

• 2.861

Base e and ln

• 'ln' stands for natural logarithm

• A natural logarithm is just a log with a base of 'e'

• If  $y=e^x$ , then  $x=\log_ey$  

•  $x=\log_ey$  can also be written as  $x=\ln y$  

Definition of the Natural Base e

•  $e\approx2.71828182846$  
  

• The natural base e is irrational 

Exponential Growth vs. Exponential Decay

-A natural base exponential function is in the form y=ae^rx

Multiple Choice

 $f\left(x\right)=e^{-3x}$  

Is the function above an exponential growth or decay?

• Exponential Decay

• Exponential Growth

• None

Simplifying Natural Base Expressions

• a) Multiplying with the same base then we can add the exponents

• b) When dividing you subtract the exponents

• c) A power to a power means you multiply the powers.

Multiple Choice

Simplify the following: $e^5\cdot e^7$  

•  $e^{12}$  

•  $e^2$  

•  $e^7$  

•  $e^{-2}$  

Multiple Choice

Simplify the following: $\frac{12e^4}{3e^3}$  

•  $4e^7$  

•  $9e^2$  

•  $4e$  

•  $9e$