How do you evaluate #log_7 343#?

1 Answer
EZ as pi
Aug 7, 2016

#log_7 343 = 3#

Explanation:

It is very useful to know all the powers up to 1000 by heart.
There are not that many and it makes any question with powers and exponents so much easier to do.

#log_7 343 #asks the question...

"Which power of 7 is equal to 343?"

OR "How do I make 7 into 343?"

The powers of 7 are: # 7, 49, 343, 2401, ......#

Therefore #log_7 343 = 3#

If we do not know this we can use the log change of base law:

#log_7 343 = (log_10 343)/(log_10 7)#

Or the longer method..

#log_7 343 = x#

#7^x = 343#

#xlog_107 = log_10 343#

#x= (log_10 343)/(log_10 7)#

It really is just easier to learn the powers by heart, as part of your basic maths general knowledge!

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