Estimate the value of the logarithm to the nearest tenth.
log7 (55)
Options
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A. 0.5
B. 2.1
C. -2.6
6.0
Answer is: 2.05
Rounded: 2.1
looks ok to me.
Why did the logarithm bring a ladder to the party?
Because it wanted to calculate the value of logarithms to the nearest tenth!
Now, let's estimate the value of the logarithm log7(55). It's going to be between two numbers: 2 and 3. Since the options given don't include 2 or 3, we can eliminate them.
Looking at the remaining options:
A. 0.5 - Nope, that doesn't even come close.
B. 2.1 - Nope, still not close enough.
C. -2.6 - Hmm, too far in the negative direction.
That leaves us with only one option, my friend:
D. 6.0 - Well, we're not climbing that high up! So, the answer is none of the above!
Hope that gave you a good laugh! Let me know if you have any other questions.
To estimate the value of the logarithm to the nearest tenth, we can use the fact that the logarithm is the exponent to which the base must be raised to obtain the given number.
In this case, we want to find the value of log7 (55).
To estimate this value, we need to determine the power to which 7 must be raised in order to get close to 55.
Let's start by trying different powers of 7:
7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
Since 7^2 = 49 and 7^3 = 343, we can estimate that 55 is between these two values.
Therefore, the value of log7 (55) is between 2 and 3.
Rounding to the nearest tenth, the value of log7 (55) is approximately 2.2.
So, the estimated value to the nearest tenth is option B. 2.1.
To estimate the value of the logarithm log7 (55) to the nearest tenth, we can use the fact that logarithms represent the exponent to which the base (in this case, 7) must be raised to equal the given number (in this case, 55).
To estimate the value, we can check the powers of 7 and determine between which two powers of 7 the number 55 falls.
Let's calculate a few powers of 7:
7^0 = 1
7^1 = 7
7^2 = 49
7^3 = 343
From these calculations, we can see that 55 falls between 49 (7^2) and 343 (7^3).
Since the question asks for the estimate to the nearest tenth, we can conclude that log7 (55) is between 2 and 3.
Now let's review the given options:
A. 0.5: Since 0.5 is less than 2 and not between 2 and 3, we can eliminate this option.
B. 2.1: 2.1 is between 2 and 3, so it is a potential answer.
C. -2.6: Since logarithms are always positive, we can eliminate this option.
D. 6.0: 6.0 is not between 2 and 3, so we can eliminate this option.
Out of the remaining options, B. 2.1 is the closest estimate to the value of log7 (55). Therefore, the answer is B. 2.1.