Evaluate log of log of 10^100000

Problem

(log_)((log_)(10))

Solution

1. Identify the base of the logarithm. In most contexts, (log_)() without a specified base refers to the common logarithm, which is base 10

2. Apply the property of logarithms (log_b)(bx)=x to the inner expression.

3. Substitute the value of the inner logarithm into the outer expression.

(log_)(10)=100000

4. Evaluate the remaining logarithm by expressing the argument as a power of 10

100000=10

5. Apply the property (log_10)(10)=5 to find the final value.

Final Answer

(log_)((log_)(10))=5

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