Incorrect Evaluation of Logarithmic Expressions
The image shows a multiple-choice question asking which of the following logarithmic expressions have been evaluated correctly, to the nearest hundredth:
A) \(\log_2 8 = 0.43\)
B) \(\log_5 63 = 1.63\)
C) \(\log_5 5 = 1.16\)
D) \(\log_2 32 = 1.51\)
Let's check each of the given logarithmic expressions one by one:
A) \(\log_2 8\)
The base-2 logarithm of 8 actually equals 3, because \(2^3 = 8\).
So, this is incorrect.
B) \(\log_5 63\)
Using a calculator or logarithm tables to find the value of \(\log_5 63\) to two decimal places, you would see the actual value is around 2.80, not 1.63.
So, this is incorrect.
C) \(\log_5 5\)
Given the fact that any log base itself is equal to 1 (\(\log_b b = 1\) for any b > 0), \(\log_5 5\) equals 1 exactly, not 1.16.
So, this is incorrect.
D) \(\log_2 32\)
The base-2 logarithm of 32 actually equals 5, since \(2^5 = 32\).
So, this is incorrect.
None of the provided logarithmic expressions are evaluated correctly. Your next steps depend on the context in which this question was asked; it may be a matter of revisiting the definitions and properties of logarithms or reporting an issue with the question if it were intended that one of the answers be correct.
