Exponential And Logarithmic Equations Worksheet With Answers Page 2
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1
2Solving Exponential and Logarithmic Equations: Answers
Exponential Equation:
−
=
2
x
3
4
e
40
Divide both sides by 4 to isolate the exponential portion
−
2
x
3
=
e
10
Take ln of both sides (use ln because the base is “e”)
−
2
x
3
=
ln
e
ln
10
Use the law of logs that allows you to bring the power into coefficient position
−
=
Recall that ln e is equivalent to 1, so the equation is actually →
2 (
x
) 3
ln
e
ln
10
−
=
2
x
3
ln
10
Now just solve for x using algebra
=
+
2
x
3
ln
10
(add 3 to both sides, then divide both sides by 2)
3 +
ln
10
=
≈ 2.651
x
2
Logarithmic equation
+
−
=
−
log
(
x
) 1
2
log
(
x
) 1
Move log terms to one side, non-log terms to other side
5
5
+
−
−
=
log
(
x
) 1
log
(
x
) 1
2
Use laws of logs to write a single log expression
5
5
+
x
1
=
log
2
Rewrite in exponential form
5
−
x
1
+
x
1
=
2
5
Solve using algebra techniques
−
x
1
+
x
1
−
25 =
Multiply both sides by
x
1
−
x
1
−
=
+
25
(
x
) 1
x
1
Use the distributive property to remove parenthesis
−
=
+
25
x
25
x
1
Subtract an x from both sides, add 25 to both sides
24 =
x
26
Divide by 24
26
13
=
=
x
Always reduce answers to lowest terms
24
12
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