Evaluate log base 3 of log base 2 of 8

Problem

(log_3)((log_2)(8))

Solution

1. Identify the inner expression, which is (log_2)(8)

2. Rewrite the number 8 as a power of 2 to simplify the inner logarithm.

8=2^3

3. Evaluate the inner logarithm using the property (log_b)(b^x)=x

(log_2)(2^3)=3

4. Substitute the result back into the outer logarithm.

(log_3)(3)

5. Evaluate the outer logarithm using the property (log_b)(b)=1

(log_3)(3)=1

Final Answer

(log_3)((log_2)(8))=1

Want more problems? Check here!