MHB (ask) Calculating Logarithmic Question

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May I know how to calculate this question without a calculator? The final answer of this question is 3 but I really have no idea how to work on it to get the final answer.

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Jdtbtb_sp said:
May I know how to calculate this question without a calculator? The final answer of this question is 3 but I really have no idea how to work on it to get the final answer.

View attachment 11006
Is it something to do with the changing base formula? I have tried using the changing base formula, hoping through this I could simplify it but it went even complicated. Then I was stuck, don't know how to solve it...
 
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Even if you change all the logarithms to the same base there is not going to be any simple way to calculate that "log(log)" without a calculator. That's why calculators were invented!
 
Country Boy said:
Even if you change all the logarithms to the same base there is not going to be any simple way to calculate that "log(log)" without a calculator. That's why calculators were invented!

Thank you for replying. Next time I should use a calculator for such a "log(log)" question. Thank you for spending time to answer my post.
 

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