Evaluate the logarithm using the change of base formula. Round to 3 decimal places.
A) 3.738
B) 1.921
C) 0.521
D) 7.273
E) 1.623

Question

Evaluate the logarithm  using the change of base formula. Round to 3 decimal places.
A) 3.738 
B) 1.921 
C) 0.521 
D) 7.273 
E) 1.623

Quizplus · Accepted Answer

Using the change of base formula, we have:
log base 10 of 11eb11e8_19b5_02d7_ad38_11a538774700_TB4588_11 = log base 2 of 11eb11e8_19b5_02d7_ad38_11a538774700_TB4588_11 / log base 2 of 10
Since log base 2 of 10 = log base 10 of 10 / log base 10 of 2 = 1 / 0.3010 ≈ 3.3219,
we get:
log base 10 of 11eb11e8_19b5_02d7_ad38_11a538774700_TB4588_11 ≈ log base 2 of 11eb11e8_19b5_02d7_ad38_11a538774700_TB4588_11 / 3.3219
Using a calculator, log base 2 of 11eb11e8_19b5_02d7_ad38_11a538774700_TB4588_11 = 5.283, so
log base 10 of 11eb11e8_19b5_02d7_ad38_11a538774700_TB4588_11 ≈ 5.283 / 3.3219 ≈ 1.921 (rounded to 3 decimal places).
Therefore, the answer is B.

Evaluate the Logarithm Using the Change of Base Formula