Evaluate Exp & Log Expressions
Solve Exponential Equations
Solve Logarithmic Equations
Expand & Condense
Logarithms
True / False
100
#1 a)
1,877
100
#2 a)
x = 1
100
#3 a)
x = 728
100
#4 a)
ln5 + 1/2ln2 + 1/2lnx - ln3 - 2/3lny
100
y = -3 (2)^(x+5) +7 has the following transformations: - horizontal shift left 5 - vertical reflection - vertical shift up 7 - horizontal stretch by 3
False (vertical stretch by 3)
200
#1 b)
51.2138
200
#2 b) Solve completely for x, then round to 4-dec places.
x = ln(12)/2 which is approximately equal to 1.2425
200
#3 b) Solve for x completely, then round to 4-dec places.
x = e^6 / 4 which is approximately equal to 100.8572
200
#4 b)
log(base7)2 - log(base7)x + 1/2log(base7)y
200
Every exponential equation has a horizontal asymptote.
True
300
#1 c)
-0.1845
300
#2 c) Solve complete for x, then round to 4-dec places.
x = 3 / (1 - ln625) which approximately equals -0.5517
300
#3 c) Don't forget to check for extraneous solutions!
x = 4, x = -2 (extraneous)
300
#5 a)
log(12y^3/2)/x
300
The change base formula allows you to change the base of any log to another base.
True.
400
#1 d)
9.3892
400
#2 d) Solve for x completely, then round to 4-dec places.
ln(96) / ln(9/2) which is approximately equal to 3.0346
400
#3 d)
x = 41/8 or x = 41.125
400
#5 b)
log(base5)1/(8a^8)
400
Exponential and logarithmic functions are inverses of each other.
True
500
Evaluate: 2log14 - 2 / e^2
1.7509
500
2^(x-3) = 11^(2-x)
x = (ln121 - ln8) / (ln2 + ln11) which is approximately equal to 2.2242
500
#3 e)
x = 216
500
Condense: 1/4log81v^8 - 3log2w^(-1) + 4log2v^3
log(6v^14w^3)
500
The range of y = 2log(x) + 3 is x > 3.
False. The range of every logarithmic function is all real numbers, just as the domain of every exponential function is all real numbers.
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