How do you evaluate #log_10(log_2[log_3 9])= x#?

1 Answer
Alan N.
Mar 14, 2016

#x = 0#

Explanation:

#If log_n x = a# Then #x = n^a#

In the question x is equal to a nest of log functions of different bases as follows:

#a = log_3 9#
#b = log_2 a#
#x = log_10 b#

Taking each in turn:

#a = log_3 9 = 2# Since #9 = 3^2#
#b = log_2 2 = 1# Since #2 = 2^1#
#x = log_10 1 = 0# Since #1 = 10^0#

Hence #x = 0#

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