Notes 7.4: Logarithmic Basics
What is an exponential function?
When we have a variable in the exponent spot of an equation, it is an
exponential function.
EX: 2x = 6
32x-7 = 98
72x = 54
“the ‘ex’ is in the ‘exponent’” 
What is the log function?
Well, we would be able to figure out given 2x = 4 that x = 2. Also, given
3x = 27 that x = 3. What about 2x = 6? What about 3x = 15? What would we
normally do to solve for a variable (like 3x + 7 = 19)? Opposite operations!
What is the opposite operation for an exponential function? A LOG function!
Logby = x
How does this help us?
Translating between forms:
EX:
Exponential form:
Log form:
bx = y
Logby = x
Evaluating logs (for now):
Because our calculators only recognize base ___________, we have to change
the log equations into exponential equations to solve.
EX: a) log464
b) log50.2
c) log 1 125
d) log366
5
Common Logs vs. natural logs:
The only difference between the two is the base. A COMMON LOG has a base
10, a NATURAL LOG has a base e.
Common Log
Natural Log
Log10x = log x
logex = ln x
These two logs can be found using the calculator.
EX: log 8 =
ln 0.3 =
log 15 =
ln 5.72 =