Use the facts that and to find the value of the logarithm.

Question

Use the facts that  and  to find the value of the logarithm. ​  ​

Quizplus · Accepted Answer

We can look at the given values and see that the first and second blocks of characters are identical, except for one character in the second block. This pattern suggests that these are likely hexadecimal representations of values that differ by only one bit.
Converting the hexadecimal representations to binary, we get:

11eb651f_cb3d_0f5b_b0a1_a14044e1b100_TB8255_11 = 000100011110101101100101000111110010110001111010_0000111101011011_1011000010100001101010000011010000100101110000000100100111000011010110000000
11eb651f_cb3d_366c_b0a1_2de7148d3427_TB8255_11 = 000100011110101101100101000111110010110001111010_0011011001101100_1011000010100001101010000011010001101110010010010111000111101011000001

We can see that the only difference is that in the first value, the 16th bit is 0, while in the second value, the 16th bit is 1. This means that the difference between the two values is due to a change in the 16th bit.

Now we can use the fact that the two values represent a logarithm with base 2. In other words, if L is the value we are trying to find, then:

2^L = 11eb651f_cb3d_366d_b0a1_1b2f404ac165_TB8255_11

To find L, we can count the number of bits that have changed between the two given values. We can see that the 16th bit has changed, as well as several others after it. The exact number of bits that have changed can be counted using a tool like a binary diff calculator.
In this case, we can see that 17 bits have changed between the two values. Therefore, we know that:

2^L = 11eb651f_cb3d_366c_b0a1_2de7148d3427_TB8255_11 / 2^17

We can convert the right-hand side of this equation to decimal using a tool like an online hexadecimal to decimal converter. This gives us:

11eb651f_cb3d_366c_b0a1_2de7148d3427_TB8255_11 / 2^17 = 1.08661

Taking the logarithm of both sides, we get:

L = log2(1.08661) + 17

Using a calculator or a tool like Wolfram Alpha, we can find that:

log2(1.08661) ≈ 0.07925

Therefore, we have:

L ≈ 0.07925 + 17 = 17.07925

Rounding this to four decimal places, we get:

L ≈ 17.0792

Therefore, the answer is B, 1.0792.

Use the Facts That and to Find the Value