Posted by Ed on Wednesday, September 8, 2010 at 4:46pm.
Find the value of the following.
10^(10log3)
The log exponent is confusing me. Could someone please help me? Thanks.

Math  bobpursley, Wednesday, September 8, 2010 at 5:00pm
10log3= log3^10= log (1/3^10)
so 10^(log(1/3^10)= 1/3^10
Here is an unconfusing explanation.
log100=2
so 10^2=l0^(log100) by definition.

Math  Reiny, Wednesday, September 8, 2010 at 5:07pm
Have you come across the property of logs that says ..
a^log_{a} k = k
your question fits that pattern after a quick adjustment
10^(10log3)
= 10^(log 3^(10))
= 3^10
= 1/3^10 , so far no calculator
= appr. .000016935
check:
log3 = .47771213
10log3 = 4.771213
10^4.771213 = .00016935

Math  Ed, Wednesday, September 8, 2010 at 8:50pm
Thanks!
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