Evaluate log base 27 of 3

Problem

(log_27)(3)

Solution

1. Identify the logarithmic expression and set it equal to an unknown variable x

(log_27)(3)=x

2. Rewrite the equation in its equivalent exponential form using the definition (log_b)(a)=c⇔bc=a

27=3

3. Express both sides of the equation with a common base, noting that 27=3

(3)x=3

4. Apply the power of a power rule (am)n=a(m*n) to simplify the left side.

3(3*x)=3

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

3*x=1

6. Solve for x by dividing both sides by 3.

x=1/3

Final Answer

(log_27)(3)=1/3

Want more problems? Check here!