SME
Grade 11 Math · Algebra 2
Logarithms and log properties
Use this for “Evaluate log₂ 32,” or rewrite a logarithm as an exponential equation.
Chart
Zero: x = 1
Vertical asymptote x = 0
Domain: (0, ∞)
f(32) = 5
This is an example. Type your own values to start a new problem.
log
(
x
)
=
y
Formulas
x
=
b
y
32
=
2
5
Assumptions
•
A log is an exponent: logb(x) is the power of b that makes x, so logb(x) = y means bʸ = x.
•
Only a positive x has a log.
•
The base b is positive and not 1.
Step-by-step
WE KNOW
b = 2, x = 32
FIND
logarithm (y)
Step 1 · Find logarithm (y)
Use x = bʸ
Ask:
b
to
what
power
makes
x
?
y
=
log₂
x
y
=
log₂
32
2
5
=
32,
so
log₂
32
=
5
y
=
5
Check
Put the numbers back in. Both sides should match.
32
=
2
5
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.