Evaluate log base 9 of 729

Problem

(log_9)(729)

Solution

1. Identify the base and the argument of the logarithm. The base is 9 and the argument is 729

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

(log_9)(729)=x

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

9=729

4. Express both sides of the equation using a common base. Since 9=3 and 729=3 we can rewrite the equation.

(3)x=3

5. Simplify the left side using the power of a power rule.

3(2*x)=3

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

2*x=6

7. Solve for x by dividing both sides by 2

x=3

Final Answer

(log_9)(729)=3

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