Match each logarithm to its value. A log 3 Logarithm N is equal to -3. B. 1093, 27 Logarithm is equal to z c. log, 27 Logarithm is equal to log, 27 3 D. Logarithmy is equal to 3.

Mathematics Questions

Match each logarithm to its value. A log 3 Logarithm N is equal to -3. B. 1093, 27 Logarithm is equal to z c. log, 27 Logarithm is equal to log, 27 3 D. Logarithmy is equal to 3.

Short Answer

The process of evaluating logarithmic expressions involves understanding their structure and using the property that relates exponential forms to logarithmic values. The evaluated results are: log‚ÄöCc‚ÄöCC‚ÄöCa‚ÄöCe(3) = 1/3, log‚ÄöCc‚ÄöCa‚ÄöCA‚ÄöCe(27) = 3/4, log‚ÄöCc‚ÄöCa‚ÄöCe(27) = 3/2, and log‚ÄöCc‚ÄöCA/‚ÄöCE‚ÄöCe(27) = -3.

Step-by-Step Solution

Step 1: Understand the Logarithmic Expressions

Begin by recognizing the structure of logarithmic expressions, which express the exponent that a base number must be raised to in order to achieve a given value. This is crucial for evaluating the logs presented. Each expression will follow the form log_base(value).

Step 2: Evaluate Each Logarithm

Evaluate the logarithmic expressions one by one by using the property that states if x = b^y, then log_b(x) = y. Here are the evaluations:

A. log₂₇(3) = 1/3 because 27^(1/3) = 3
B. log₈₁(27) = 3/4 because 81^(3/4) = 27
C. log₉(27) = 3/2 because 9^(3/2) = 27
D. log_1/3(27) = -3 because (1/3)^(-3) = 27

Step 3: Recap and Use the Results

Finally, summarize the outcomes from your evaluations for clarity and reference. Knowing these values allows you to understand how the logarithmic functions relate to their bases:

A. log₂₇(3) = 1/3
B. log₈₁(27) = 3/4
C. log₉(27) = 3/2
D. log_1/3(27) = -3

Match each logarithm with its corresponding value: A) log(3) = …