Expand the Logarithmic Expression log base 3 of 1/27

Problem

(log_3)(1/27)

Solution

1. Identify the expression as a logarithm with base 3 and an argument that is a fraction.

2. Apply the quotient rule for logarithms, which states that (log_b)(x/y)=(log_b)(x)−(log_b)(y)

(log_3)(1/27)=(log_3)(1)−(log_3)(27)

3. Evaluate the first term using the property that (log_b)(1)=0 for any base b

(log_3)(1)=0

4. Rewrite the number 27 as a power of the base 3 to simplify the second term.

27=3

5. Substitute the power back into the expression and apply the power rule (log_b)(bk)=k

(log_3)(3)=3

6. Subtract the evaluated terms to find the final value.

0−3=−3

Final Answer

(log_3)(1/27)=−3

Want more problems? Check here!