1. Logs Review/Practice

2. Logs Review/Practice
If “x” is the argument of a log, and “b” is the base of a log, then:
logb x = y  by = x
The natural log of x, is the log “base e” of x (written either loge x or ln x):
ln x = y  ey = x
Logs and exponential functions are inverses (e.g., “undo” each other)
A “log” is an exponent. Specifically, it’s the exponent of the base that yields the argument of the log.
e is a special number (like p), having a value of … (non- repeating decimal)
eln x = x
ln (ex) = x
eln (-3x) = -3x
ln (ebz) = bz

3. Logs Review/Practice Solve for x: b = e-ax Solve for x: ln x = b
  ln b = ln e-ax
  eln x = eb
  ln b = -ax
  x = eb
  ln b = x
 -a

4. Logs Review/Practice ln a + ln b Simplify: ln(ab) = Simply: ln(bc) =
c ln b

5. Logs Review/Practice
Solve for x by taking the ln of both sides: d = Aebx
  ln d = ln Aebx
  ln d = ln A + ln ebx
  ln d = ln A + bx
  ln d - ln A = bx b
  ln d - ln A = x

6. Logs Review/Practice Solve for m: 7.8 = 2.0m   ln 7.8 = ln 2.0m
  ln 7.8 = m ln 2.0
  m = 2.96…