(ask) Calculating Logarithmic Question

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SUMMARY

The discussion centers on calculating the expression log_2(log_3(65)) + 3*log_5(log_5(9)), which is claimed to equal 3. Participants highlight the challenges of evaluating logarithmic expressions without a calculator, particularly when dealing with nested logarithms. The consensus is that while the answer may be provided in textbooks, practical evaluation often yields different results, such as 2.506, due to rounding errors. The changing base formula does not simplify the calculation effectively.

PREREQUISITES
  • Understanding of logarithmic functions and properties
  • Familiarity with the changing base formula for logarithms
  • Basic knowledge of numerical approximation techniques
  • Experience with mathematical software like Wolfram Alpha
NEXT STEPS
  • Study the properties of logarithms, focusing on nested logarithmic expressions
  • Learn how to apply the changing base formula in various contexts
  • Explore numerical approximation methods for evaluating complex logarithmic expressions
  • Investigate the use of mathematical software tools for solving logarithmic equations
USEFUL FOR

Students, educators, and anyone interested in advanced mathematics, particularly those dealing with logarithmic calculations and numerical evaluations.

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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...
 
Last edited:
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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