How do I find the value of this logarithmic expression without using a calculator? I'm trying to relearn algebra, but this problem has me scratching my head, and my Google tutorial searches are failing me.
$2^{\log_2 10}$
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$\begingroup$ What is the base of the log? $\endgroup$ – lab bhattacharjee Aug 31 '14 at 13:11
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$\begingroup$ Sorry, the base is 2 $\endgroup$ – programmer Aug 31 '14 at 13:28
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$\begingroup$ Just as a sidenote, the original wording had "lg" which I've seen used as notation for log base 2. $\endgroup$ – Mike Aug 31 '14 at 14:00
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If the base of the logarithm is $10$:
Using the identity $\log_a a=1$ we have the following:
$$2^{\log_{10} {10}}=2$$
If the base of the logarithm is $2$:
Using the identity $a^{\log_a x}=x$ we have the following:
$$2^{\log_{2} {10}}=10$$
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If you meant $2^{\log_2{10}}$, then the answer is simply $10$:
$\log_2{10}$ means, a value $x$ such that $2^x=10$.
So if you take this $x$ and calculate $2^x$, then you will obviously get $10$.
answered Aug 31 '14 at 13:14
