Question - Incorrect Evaluation of Logarithmic Expressions
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Solution:
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.
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