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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