Question 539106
evaluate the expression 
log base 4 (log base 3 81) 
looks like log4(log3 81)



log base 4 (log base 3 81) 


We have to evaluate in two parts:


First (log base 3 81) 


We know that 81 = 3^4, So


Log base 3 3^4


We know that Log base A of A^b = b*Log base A of A


So 


Log base 3 3^4 = 4*Log base 3 of 3


4*Log base 3 of 3 = 4*1
4*Log base 3 of 3 = 4


Then (log base 3 81) = 4



Now, log base 4 (log base 3 81) = log base 4 (4)  


Using the main property of Logarithms: Log base A of A = 1



log base 4 of (4)  = 1



The answer is: log base 4 (log base 3 81) = 1



Any questions, please ask me.