MHB (ask) Calculating Logarithmic Question

[Jdtbtb_sp]

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.

 

[Jdtbtb_sp]

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...

 

[skeeter]

Wolfram Alpha & my calculator do not get an evaluation that equals 3 ...

log_2(log_3(65)) + 3*log_5(log_5(9)) - Wolfram|Alpha

 

[HOI]

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!

 

[Jdtbtb_sp]

Wolfram Alpha & my calculator do not get an evaluation that equals 3 ...

log_2(log_3(65)) + 3*log_5(log_5(9)) - Wolfram|Alpha

View attachment 11007

The answer given in my book is 3. I used a calculator and it also gave me 2.506 as well, perhaps it is because of rounding off.

 

[Jdtbtb_sp]

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.