7-7 Base e and Natural Logarithms
Write an equivalent exponential or logarithmic
function.
25. ln (x + 4) = 36
2
33. 3 ln x + 4 ln 3
SOLUTION: SOLUTION: 26. e
−2
=x
6
SOLUTION: Solve each equation. Round to the nearest tenthousandth.
37. −2e
3x
+ 19 = 3
SOLUTION: Write each as a single logarithm.
30. SOLUTION: The solution is 0.6931.
38. 6e
4x
+7=4
SOLUTION: Logarithm is not defined for negative values.
Therefore, there is no solution.
39. −4e
−x
+9=2
SOLUTION: 2
33. 3 ln x + 4 ln 3
SOLUTION: eSolutions Manual - Powered by Cognero
Solve each equation. Round to the nearest tenthousandth.
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Logarithm
not defined
for negative values.
7-7 Base
e andisNatural
Logarithms
Therefore, there is no solution.
39. −4e
−x
The solutions are {x | x ≤ 2.1633}.
4
45. ln (8x ) > 24
+9=2
SOLUTION: SOLUTION: The solution is –0.5596
The solutions are
Solve each inequality. Round to the nearest tenthousandth.
x
41. e ≤ 8.7
SOLUTION: .
Write the expression as a sum or difference of
logarithms or multiples of logarithms.
4 −3
51. ln xy z
SOLUTION: x
The solutions are {x | x ≤ 2.1633}.
x+1
58. CHALLENGE Solve 4 − 2
= 15 for x.
SOLUTION: 4
45. ln (8x ) > 24
SOLUTION: x
Let 2 = y
By the Zero Product Property:
The solutions are
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.
Write the expression as a sum or difference of
logarithms or multiples of logarithms.
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SOLUTION: 7-7 Base e and Natural Logarithms
x
x+1
58. CHALLENGE Solve 4 − 2
= 15 for x.
SOLUTION: x
Let 2 = y
By the Zero Product Property:
Logarithms are not defined for negative values.
Therefore,
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