Find the value of the following.

Question

10^(-10log3)

The log exponent is confusing me. Could someone please help me? Thanks.

Answer 1

-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.

Answer 2

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

Answer 3

Thanks!