http://www.ck12.org Chapter 6. Transcendental Functions
Before we move to the calculus of exponential and logarithmic functions, here is a summary of the two important
relationships that we have just discussed:
- The functiony=bxis equivalent tox=logbyify>0 andx∈R.
- The functiony=exis equivalent tox=lnyify>0 andx∈R.
You should also recall the following important properties about logarithms:
- logbvw=logbv+logbw
- logbwv=logbv−logbw
- logbwn=nlogbw
- To express a logarithm with base in terms of the natural logarithm: logbw=lnlnwb
- To express a logarithm with basebin terms of another basea: logbw=loglogaawb
Review Questions
Solve forx.
- 6x= 2161
2.ex= 3 - log 2 z= 3
- lnx^2 = 5
- 3e−^5 x= 132
6.e^2 x− 7 ex+ 10 = 0
7.− 4 ( 3 )x=− 36 - lnx−ln 3= 2
9.y=5 log 10 ( 2 −^2 x)
10.y= 3 e−^2 x/^3