Question

question
what is the value of \\(\log_{9} 729\\)?

answer attempt 1 out of 2

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Explanation:

Step1: Recall logarithm definition

Let \( \log_{9} 729 = x \). By definition of logarithm, this means \( 9^x = 729 \).

Step2: Express 729 as power of 9

We know that \( 9 = 9^1 \), \( 9^2 = 81 \), \( 9^3 = 9\times9\times9 = 729 \). So \( 9^x = 9^3 \).

Step3: Solve for x

Since the bases are equal, the exponents must be equal. So \( x = 3 \).

Answer:

3