Evaluate log base 3 of 6561

Problem

(log_3)(6561)

Solution

1. Identify the logarithmic expression as an equation where x is the exponent such that the base 3 raised to x equals 6561

(log_3)(6561)=x

2. Rewrite the equation in exponential form.

3=6561

3. Factor the number 6561 into powers of 3 by repeated division.

6561=3⋅2187

6561=3⋅729

6561=3⋅243

6561=3⋅81

6561=3⋅27

6561=3⋅9

6561=3⋅3

6561=3

4. Equate the exponents since the bases are now the same.

3=3

x=8

Final Answer

(log_3)(6561)=8

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