If log 36 ≈ 1.556, what is log 6 to the nearest thousandth? (1 point)
Responses
0.519
0.778
1.248
0.259
If log 36 ≈ 1.556, what is log 6 to the nearest thousandth? (1 point)
Responses
0.519
0.778
1.248
0.259
which one is the correct answer
The correct answer is 0.778.
If log x ≈ 0.698, what is log( x ⋅ x ⋅ x )? (1 point)
Responses
2.094
−0.34
0.34
−2.094
which one is the correct answer
To find log(x ⋅ x ⋅ x), we can use the logarithmic property that states log(a ⋅ b) = log(a) + log(b).
Starting with log(x ⋅ x ⋅ x), we can rewrite it as log(x) + log(x) + log(x).
Now, let's substitute the given approximation for log x (0.698) into the equation:
log(x ⋅ x ⋅ x) ≈ log(x) + log(x) + log(x)
log(x ⋅ x ⋅ x) ≈ 0.698 + 0.698 + 0.698
Simplifying the equation:
log(x ⋅ x ⋅ x) ≈ 2.094
So, the correct answer is 2.094.
Which of the following rewritten logarithms uses the Power Rule of Logarithms to evaluate log 10 4/5? (1 point)
Responses
−4/5 log 10
negative Start Fraction 4 over 5 End Fraction
−5/4 log 10
negative Start Fraction 5 over 4 End Fraction
4/5 log 10
Start Fraction 4 over 5 End Fraction
5/4 log 10
which one is the correct answer
The correct answer is 4/5 log 10.
Which of the following is equal to log 2 8 4/3 ? (1 point)
Responses
4
9/4
16/3
64/3
which one is the correct answer
To find log 6, we can use the logarithmic property that states log a + log b = log (ab).
Starting with log 6, we can rewrite it as log (2 * 3) since 6 = 2 * 3.
Next, we can use the logarithmic property to separate the log expression into two separate logarithms:
log 6 = log 2 + log 3
Now, let's substitute the given approximation for log 36 (1.556) into the equation:
log 6 ≈ log 2 + log 3
log 6 ≈ 1.556 + log 3
Since we only need to find log 6 to the nearest thousandth, we can just focus on the decimals.
log 6 ≈ 0.556 + log 3
To find log 3, we can use the same approximation log 36 ≈ 1.556 and rewrite it as log (6 * 6) = 2 * log 6 ≈ 2 * 1.556 = 3.112.
Now, substitute this approximation into the equation:
log 6 ≈ 0.556 + 3.112
log 6 ≈ 3.668
To the nearest thousandth, log 6 is approximately 3.668.
So the correct answer is 3.668.
To find log2(8/3), we can use the logarithmic identity that states log(base a)(b/c) = log(base a)(b) - log(base a)(c).
Starting with log2(8/3), we can rewrite it as log2(8) - log2(3).
We know that 8 can be expressed as 2^3, so log2(8) = log2(2^3) = 3.
Therefore, log2(8/3) is equal to 3 - log2(3).
Out of the given options, the correct answer is not provided.