How do you evaluate $10^{4 {log}_{10} 2}$ $10^(4log_10 2)$ ?

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Answer 1 · 2016-12-20T00:18:48

$10^{4 {log}_{10} 2} = 16$ $10^(4 log_10 2) = 16$

By definition of ${log}_{10}$ $log_10$ , for any $t > 0$ $t > 0$ we have:

$10^{{log}_{10} t} = t$ $10^(log_10 t) = t$

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

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

So:

$10^{4 {log}_{10} 2} = {(10^{{log}_{10} 2})}^{4} = 2^{4} = 16$ $10^(4 log_10 2) = (10^(log_10 2))^4 = 2^4 = 16$

How do you evaluate 10^(4log_10 2)104log10210^(4log_10 2)?