Evaluate log base 6 of 1296

Problem

(log_6)(1296)

Solution

1. Identify the base and the argument of the logarithm. The base is 6 and the argument is 1296

2. Rewrite the expression as an equation by setting it equal to x

(log_6)(1296)=x

3. Convert the logarithmic equation into its equivalent exponential form.

6=1296

4. Determine the power of 6 that equals 1296 by testing integer exponents.

6=6

6=36

6=216

6=1296

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

6=6

x=4

Final Answer

(log_6)(1296)=4

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