Question - Logarithmic Expressions Evaluation
mathlogarithmic expressions evaluationlogarithmic expressionslogarithms calculationchange of base formula
Solution:
The image displays four options with different logarithmic expressions evaluated to two decimal places. To check which one has been evaluated correctly, we would typically calculate the value of each logarithm and compare it to the given value. Here they are evaluated:A. log₃ 8B. log₆ 6C. log₄ 5D. log₂ 32Now, let's calculate these using base-10 logarithms (common logarithms) or base-e logarithms (natural logarithms) and the change of base formula:log_b(a) = log_k(a) / log_k(b)where k is any positive real number different from 1 (like 10 or e), and we'll use a calculator to find the common logarithm (base-10) or natural logarithm (base-e) of the numbers. A. log₃ 8 = log(8) / log(3) ≈ 0.90309 / 0.47712 ≈ 1.89B. log₆ 6 = log(6) / log(6) ≈ 0.77815 / 0.77815 = 1C. log₄ 5 = log(5) / log(4) ≈ 0.69897 / 0.60206 ≈ 1.16D. log₂ 32 = log(32) / log(2) ≈ 1.50515 / 0.30103 ≈ 5Now, let's round the results to the nearest hundredth and compare them to the supplied values:A. 1.89 does not match 0.43B. 1 matches 1.63 (but note that the logarithm of a number to its own base equals 1 without the need for calculation)C. 1.16 matches 1.16D. 5 does not match 1.51As such, the only correctly evaluated expression to the nearest hundredth is:C. log₄ 5 = 1.16
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