Questions: Evaluate: log3 243 (A) 1/5 (B) 1/15 (C) 15 (D) 5

Transcript text: Evaluate: $\log _{3} 243$ (A) $\frac{1}{5}$ (B) $\frac{1}{15}$ C 15 D 5

Solution

Step 1: Rewrite 243 as a power of 3

We know that $ 243 $ can be expressed as a power of $ 3 $. Specifically, $ 243 = 3^5 $.

Step 2: Substitute into the logarithm

Substitute $ 243 = 3^5 $ into the logarithm expression: \[ \log_3 243 = \log_3 (3^5). \]

Step 3: Apply the logarithm power rule

Using the logarithm power rule $ \log_b (b^x) = x $, we simplify: \[ \log_3 (3^5) = 5. \]

Step 4: Match the result with the given options

The result $ 5 $ corresponds to option (D).

$\boxed{5}$

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