Solve 3log25 - log34 + log2(log39): 6.335

[rogerfreak]

This question should be easy to most people here and need some help on this question.

3log25 - log34 + log2(log39)

My answer to this question is:
= 3log25 - log34 + log2(log9/log3)
= log2125 - log34 + log22
= log2125 - log34 + 1
= (log125 / log2) - (log4 / log3) + 1
= 6.703924778

However the correct answer give is 6.335, which means my answer is wrong. Can somebody tell me what's wrong with my answer and what should I do to get the correct answer?

Thanks :)

 

[Zurtex]

These steps you have made do not make any sense:

$$\log_2 \log_2 9 \Rightarrow \log_2 \left( \frac{\log 9}{\log 3} \right) \Rightarrow \log_2 2$$

 

[rogerfreak]

opps...sorry. i had a typo in my post. edited it

it should be:
$$\log_2 \log_3 9 \Rightarrow \log_2 \left( \frac{\log 9}{\log 3} \right) \Rightarrow \log_2 2$$

but i still cannot solve this equation. :(

 

[Zurtex]

Well in that case your reduction of the logs is perfectly correct and your approximation to the number in decimal places is also correct. The number is about:

6.7039247775191721694119040597826488189953228988...