A. 0.051
B. 0.778
C. 0.861
D. 1.857
Don't tell me to put in calculator.
B. 0.778
C. 0.861
D. 1.857
Don't tell me to put in calculator.
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You don't need a calculator. You need to know the rules of logarithms and you need to know how to factor numbers
log(a^b) = b * log(a)
log(a * b) = log(a) + log(b)
log(a/b) = log(a) - log(b)
log(72) =>
log(8 * 9) =>
log(8) + log(9) =>
log(2^3) + log(3^2) =>
3 * log(2) + 2 * log(3) =>
3 * 0.301 + 2 * 0.477 =>
0.903 + 0.954 =>
1.857
log(a^b) = b * log(a)
log(a * b) = log(a) + log(b)
log(a/b) = log(a) - log(b)
log(72) =>
log(8 * 9) =>
log(8) + log(9) =>
log(2^3) + log(3^2) =>
3 * log(2) + 2 * log(3) =>
3 * 0.301 + 2 * 0.477 =>
0.903 + 0.954 =>
1.857
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For this answer, no real calculations are required. Since the log function on a calculator is to base 10, the question would look like this:
10^x = 72
10 to the power of anything smaller than 1 would give you an answer that would be less than 10. There is only one answer above that has an exponent larger than 1. The answer is D.
The first part of the question is letting you know what the base of the log function is. (10^0.301=2 , 10^0.477=3)
Hope this helped.
10^x = 72
10 to the power of anything smaller than 1 would give you an answer that would be less than 10. There is only one answer above that has an exponent larger than 1. The answer is D.
The first part of the question is letting you know what the base of the log function is. (10^0.301=2 , 10^0.477=3)
Hope this helped.
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72 = 2*36 = 2 * 2 * 18 = 2 * 2 * 2 * 9 = 2 * 2 * 2 * 3 * 3
-->
72 = 2³3² (i.e. 8 * 9)
Therefore we can write:
log(72) = log(2³3²)
--> you have a multiplication of two numbers...separate using log(a * b) = log(a) + log(b)
log(2³3²) = log(2³) + log(3²)
--> now use log(a^b) = b * log(a)
log(2³) + log(3²) = 3 * log(2) + 2 * log(3)
--> now plug in your values for log(2) and log(3)
log(72) ~ 3 * .301 + 2 * .477
-->
.903 + .954 = 1.875, the answer is D)
-->
72 = 2³3² (i.e. 8 * 9)
Therefore we can write:
log(72) = log(2³3²)
--> you have a multiplication of two numbers...separate using log(a * b) = log(a) + log(b)
log(2³3²) = log(2³) + log(3²)
--> now use log(a^b) = b * log(a)
log(2³) + log(3²) = 3 * log(2) + 2 * log(3)
--> now plug in your values for log(2) and log(3)
log(72) ~ 3 * .301 + 2 * .477
-->
.903 + .954 = 1.875, the answer is D)
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You need to use the properties of logs.
log(MN) = logM + logN
log(Aˣ) = x logA
log(72) = log(2³ * 3²) = log 2³ + log 3² = 3 log 2 + 2 log 3
--------> 3 * .301 + 2 * .477 = .903 +.954 = 1.857 ---> D
log(MN) = logM + logN
log(Aˣ) = x logA
log(72) = log(2³ * 3²) = log 2³ + log 3² = 3 log 2 + 2 log 3
--------> 3 * .301 + 2 * .477 = .903 +.954 = 1.857 ---> D
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log(72)
= log(9x8)
= log(9) + log(8)
= log(3²) + log(2³)
= 2log(3) + 3log(2)
≈ 2x0.477 + 3x0.301
= 0.954 + 0.903
= 1.857
= log(9x8)
= log(9) + log(8)
= log(3²) + log(2³)
= 2log(3) + 3log(2)
≈ 2x0.477 + 3x0.301
= 0.954 + 0.903
= 1.857
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since 72 = 2*2*2*3*3
log (72) = log (2*2*2*3*3)
log (72) = log (2) + log (2) log (2) + log (3) + log (3)
log (72) = .301 + .301 +.301 +.477 +.477 = 1.857
log (72) = log (2*2*2*3*3)
log (72) = log (2) + log (2) log (2) + log (3) + log (3)
log (72) = .301 + .301 +.301 +.477 +.477 = 1.857
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log 72 =
log 8*9 =
log8 + log9 =
log2^3 + log3^2 =
3log2 + 2log3 =
3(0.301) + 2(0.477) = 1.857
Answer : D
log 8*9 =
log8 + log9 =
log2^3 + log3^2 =
3log2 + 2log3 =
3(0.301) + 2(0.477) = 1.857
Answer : D
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D
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