Expand the Logarithmic Expression log base 3 of 729

Problem

(log_3)(729)

Solution

1. Identify the base and the argument of the logarithm. The base is 3 and the argument is 729

2. Rewrite the argument as a power of the base. We check powers of 3

3=3

3=9

3=27

3=81

3=243

3=729

3. Substitute the exponential form into the logarithmic expression:

(log_3)(3)

4. Apply the power rule for logarithms, which states (log_b)(xp)=p*(log_b)(x)

6*(log_3)(3)

5. Simplify using the property (log_b)(b)=1

6⋅1=6

Final Answer

(log_3)(729)=6

Want more problems? Check here!