How do you solve #3^(n+3)=14.5#?

1 Answer
Alan P.
Apr 23, 2018

#n~~2.43115#

Explanation:

#3^(x+3)=14.5#

#rArr 3^n * 3^3=14.5#

#rArr 3^n * 27 = 14.5#

#rArr 3^n=14.5/27#

and based on the definition of logs
#rArr n=log_3 (14.5/27)#

This can be evaluated with a calculator or spreadsheet function
(for my spread sheet this would look like #=log(14.5"/"27,3)#)
to obtain the approximation:
#n~~2.4311499#

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