log base 5 of (log base 3 of x)=0

how would i solve that

Question

log base 5 of (log base 3 of x)=0 

how would i solve that

zepdrix · Answer

$$\huge \log_5 (\log_3 x)=0$$Hmm that's a weird problem :) lol

zepdrix · Answer

We can exponentiate both sides, writing them with a base of 5, because that is our outer log. That will give us,$$\huge 5^{\log_5 (\log_3 x)}=5^0$$

The Exponential and Logarithm are INVERSE operations of one another, so they will essentially "cancel out". So the 5 and LOG will cancel out ok?
Giving us,$$\huge (\log_3 x)=5^0$$Simplifying the right side gives us,$$\huge \log_3 x=1$$

zepdrix · Answer

We'll have to do something similar for the inner log, but we don't want to exponentiate with a 5, since this inner log has a base of 3.
Can you guess the next step? :o

anonymous · Answer

change it to inverse form and solve for x

anonymous · Answer

thank you so much

zepdrix · Answer

Able to finish the rest on your own? :D

anonymous · Answer

yes. thx

anonymous · Answer

could you help me with another  question