How do you solve #6^x=216#?

1 Answer
KillerBunny
Oct 13, 2016

#x=3#

Explanation:

You can decompose #216# to see its prime factors:

#216 \div 2 = 108#
#108 \div 2 = 54#
#54 \div 2 = 27#
#27 \div 3 = 9#
#9 \div 3 = 3#
#3 \div 3 = 1#

Thus, #2016 = 2^3 * 3^3#

But this means that #2016 = (2*3)^3=6^3#, and thus #x=3#

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