SME
Grade 11 Math · Algebra 2
Exponential and logarithmic equations, e and continuous growth
Use this for “Solve 5 × 2ˣ = 60” with logarithms.
Chart
Horizontal asymptote y = 0
f(x) = g(x)
The curves cross at x ≈ 3.585.
This is an example. Type your own values to start a new problem.
a
×
b
x
=
c
x
Solution
worked out (not typed)
Formulas
a
×
b
x
=
c
5
×
2
3.585
=
60
Assumptions
•
Divide by a first, then take the log of both sides: x log b = log(c ÷ a).
•
Any base works for the logs, if both sides use the same one.
•
bˣ is always positive, so c ÷ a must be positive for a solution.
Step-by-step
WE KNOW
a = 5, b = 2, c = 60
FIND
solution (x)
Step 1 · Find solution (x)
Use a × bˣ = c
Divide
by
a
,
take
the
log
of
both
sides,
then
divide
by
log
b
.
x
=
log₁₀(
c
÷
a
)
log₁₀
b
x
=
log₁₀(60 ÷ 5)
log₁₀ 2
2ˣ = 12
x
=
log₁₀ 12
log₁₀ 2
x
=
1.0792
0.301
x
=
3.585
Check
Put the numbers back in. Both sides should match.
5
×
2
3.585
=
60
✓
Topic check
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