How do you evaluate $10^(4log_10 2)$ ?

Question

2956 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-20T00:18:48

$10^(4 log_10 2) = 16$

By definition of $log_10$ , for any $t > 0$ we have:

$10^(log_10 t) = t$

Also note that for any $a, b$ we have:

$10^(ab) = (10^a)^b$

So:

$10^(4 log_10 2) = (10^(log_10 2))^4 = 2^4 = 16$

How do you evaluate 10^(4log_10 2)10^(4log_10 2)?