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All questions of Logarithms for ACT Exam
Let log 5 = 0.69897 and log 2 = 0.30103. Solve log 50- a)1.36903
- b)1.39794
- c)1.30103
- d)1.69897
Correct answer is option 'D'. Can you explain this answer?
Let log 5 = 0.69897 and log 2 = 0.30103. Solve log 50
a)
1.36903
b)
1.39794
c)
1.30103
d)
1.69897
|
Thomas Montgomery answered |
Given Information:
- log 5 = 0.69897
- log 2 = 0.30103
Calculating log 50:
- log 50 = log (5 * 10)
- log 50 = log 5 + log 10
- log 50 = 0.69897 + 1
- log 50 = 1.69897
Calculating log (50a):
- log (50a) = log 50 + log a
- log (50a) = 1.69897 + log a
Since the value of log (50a) is given as 1.69897, we can equate it to the calculated value:
1.69897 = 1.69897 + log a
log a = 0
Therefore, log (50a) = log a = 0. This means that the value of 'a' that satisfies log (50a) = 1.69897 is when a = 1.
Therefore, the correct answer is option D) 1.69897.
Evaluate log327- a)9
- b)3
- c)30
- d)10
Correct answer is option 'B'. Can you explain this answer?
Evaluate
log327
a)
9
b)
3
c)
30
d)
10
|
Orion Classes answered |
You can change the form to
3x = 27
x = 3
if log4(16) = x, what is log2(x)?- a)x = 1/2
- b)x = 1
- c)x = 0
- d)x = 2
Correct answer is option 'B'. Can you explain this answer?
if log4(16) = x, what is log2(x)?
a)
x = 1/2
b)
x = 1
c)
x = 0
d)
x = 2
|
|
Orion Classes answered |
The first step of this problem is to find
log4(16) by expanding to the formula
4y = 16.
4y = 16.
y is found to be 2. The next step is to plug y in to the second log.
log2(2), which expands to
2x = 2,
x = 1
can be written as which of the following?
A. 
B. log5 25
C. 2- a)A only
- b)A, B and C
- c)B only
- d)B and C only
Correct answer is option 'B'. Can you explain this answer?
can be written as which of the following?A.
B. log5 25
C. 2
a)
A only
b)
A, B and C
c)
B only
d)
B and C only
|
|
Orion Classes answered |
A is true in two ways. You can use the fact that if a logarithm has no base, you can use base 10, or you can use the fact that you can use this property:
B is a simple change of base application, and C is simply computing the logarithm.
Solve for x5x+1 = 60.Round to the nearest hundredth.- a)3.73
- b)1.54
- c)1.75
- d)4.73
Correct answer is option 'B'. Can you explain this answer?
Solve for x
5x+1 = 60.
Round to the nearest hundredth.
a)
3.73
b)
1.54
c)
1.75
d)
4.73
|
|
Orion Classes answered |
To solve an exponential equation like this, you need to use logarithms. This can be translated into:
log5(60) = x + 1
Now, remember that your calculator needs to have this translated. The logarithm log5(60) is equal to the following:
which equals approximately 2.54.Remember that you have the equation:
2.54 = x + 1
Thus, x = 1.54.
Solve for x in the following equation:log224 - log23 = logx27- a)1
- b)9
- c)2
- d)3
Correct answer is option 'D'. Can you explain this answer?
Solve for x in the following equation:
log224 - log23 = logx27
a)
1
b)
9
c)
2
d)
3
|
|
Orion Classes answered |
Since the two logarithmic expressions on the left side of the equation have the same base, you can use the quotient rule to re-express them as the following:
log224 – log23 = log2(24/3) = log28 = 3
Therefore we have the following equivalent expressions, from which it can be deduced that x = 3.
logx27 = 3
x3 = 27
What value of x satisfies the equation logx 64 = 2?- a)8
- b)4
- c)2
- d)10
Correct answer is option 'A'. Can you explain this answer?
What value of x satisfies the equation logx 64 = 2?
a)
8
b)
4
c)
2
d)
10
|
|
Orion Classes answered |
The answer is 8.
logx 64=2 can by rewritten as x2 = 64.
In this form the question becomes a simple exponent problem. The answer is 8 because 82 = 64.
If log4 x = 2, what is the square root of x?- a)2
- b)3
- c)4
- d)12
Correct answer is option 'C'. Can you explain this answer?
If log4 x = 2, what is the square root of x?
a)
2
b)
3
c)
4
d)
12
|
|
Orion Classes answered |
Given log4x = 2, we can determine that 4 to the second power is x; therefore the square root of x is 4.
If logx 25 = 2, then x = ?- a)25
- b)10
- c)15
- d)5
Correct answer is option 'D'. Can you explain this answer?
If logx 25 = 2, then x = ?
a)
25
b)
10
c)
15
d)
5
|
|
Orion Classes answered |
logx 25 = 2
Calculate the power of x that makes the expression equal to 25. We can set up an alternate or equivalent equation to solve this problem:
25 = x2
Solve this equation by taking the square root of both sides.
√25 = √x2
x = ± 5
x ≠ −5, because logarithmic equations cannot have a negative base.
The solution to this expression is:
x = 5
Calculate the power of x that makes the expression equal to 25. We can set up an alternate or equivalent equation to solve this problem:
25 = x2
Solve this equation by taking the square root of both sides.
√25 = √x2
x = ± 5
x ≠ −5, because logarithmic equations cannot have a negative base.
The solution to this expression is:
x = 5
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