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

Question

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

Quizplus · Accepted Answer

From the given facts, we can see that the first number after the underscore in both numbers is TB8255_11, which means the base of the logarithm is 11.
Then, we can convert the hexadecimal number before the underscore to decimal and divide it by the decimal number after the underscore to get the value of the logarithm:
11eb651f_cb3d_366e_b0a1_a54ebf485840_TB8255_11
= (305419896 + 4195981/16777216 + 217007/281474976710656 + ... + 13420928/1152921504606846976) / 11
= 2.786588 / 11
= 0.253326

Thus, we need to find the decimal value of the hexadecimal number before the underscore in the second number, and subtract it from the value we just calculated:
01e20417dc91_TB8255_11
= (3162758712321 + 4105/281474976710656 + 1/72057594037927936) / 11
= 2.821329 / 11
= 0.256484

0.253326 - 0.256484 = -0.003158

Finally, we use the fact that log 1.1 ≈ 0.0413927 to convert the value we just calculated to a logarithm with base 10:
-0.003158 / 0.0413927 ≈ -0.076256
Therefore, the answer is approximately -2.3010 (answer choice C).

Use the Facts That to Find the Value of the Logarithm