log/expoential equations precalculs

Tutor: None Selected Time limit: 1 Day

e^x times e^(x+1) = 1

a. combine the exponential expressions to a single expoential expression, 

b. convert to logarthmic eqation.

c. solve equation 

Sep 2nd, 2015

Thank you for the opportunity to help you with your question!

To combine the expression, use the law of exponents,

e^(x)* e^(x+1)=1

Gives, e^(x+x+1)=1                                                                         [Law: (x^m)* (x^n)= x^(m+n) ]

=> e^(2x+1)=1

Now to convert to log, take log of both the sides,

gives, log(e^(2x+1)) = log(1)

Using properties of logarithms,

=> (2x+1)log(e)= 0                                                                          [Laws: log(x^a)= a log(x); log(1) =0 ]

Now, to solve the equation, we have log(e)= 1,

=> 2x+1 = 0

=> x= -(1/2)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 2nd, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
Sep 2nd, 2015
Sep 2nd, 2015
Feb 21st, 2017
Mark as Final Answer
Unmark as Final Answer
Final Answer

Secure Information

Content will be erased after question is completed.

Final Answer