Lesson 7-6 Natural Logarithms

Lesson 7-6 Natural Logarithms

by Steven Giesting

Multiple Choice

Simplify the expression

$$e^7\cdot e^8$$  

• $$e^{56}$$  

• $$e$$  

• $$e^{15}$$  

• $$e^{5764801}$$  

Multiple Choice

Simplify the expression

$$\frac{28e^8}{7e^2}$$  

• $$4e^6$$  

• $$21e^6$$  

• $$4e^{10}$$  

• $$4e^4$$  

​Example 1

Fill in the Blank

Solve the equation, round to the nearest thousandth

$$e^{2x}=12$$  

Fill in the Blank

Solve the equation, round your answer to the nearest thousandth

$$e^{\frac{x}{5}}+4=7$$  

​Example 2

​Solve the equation, round your answer to the nearest thousandth

​Write the problem in exponential form

​Evaluate the left side

​Solve

Fill in the Blank

Solve the equation, round your answer to the nearest thousandth

$$\ln\ x\ =\ -\ 2$$  

​Write the expression as a single logarithm

Multiple Choice

Write the expression as a single logarithm

$$5\ln m-3\ln n$$  

• $$\ln\ 15mn$$  

• $$\ln\ \frac{n^3}{m^5}$$  

• $$\ln\ \frac{m^5}{n^3}$$  

• $$\ln\ \left(mn\right)^2$$