If $log_4 x =3$ , then what is $x$ equal to?

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Answer 1 · 2018-06-14T00:42:49

#x=3^4=81

The definition of a logarithm is that $log_a(b)=c$ iff $b=a^c$ . Using this definition, we see that $log_4x=3$ implies that $x=3^4$ , so $x=81$ .

Answer 2 · 2018-06-14T00:51:00

$x=64$

The key realization here is that if we have a logarithmic equation of the form

$log_ab=c$

That this is equal to

$a^c=b$

We essentially have $a=4, b=x$ and $c=3$ . Plugging in, we get

$4^3=x=>color(blue)(x=64)$

Another way we could have approached this is leveraging the logarithm property

$a=log_b(b^a)$

Where our $a=3$ and our $b=4$ . Plugging in, we get

$3=log_4(4^3)$

$3=log_4color(blue)((64))$

Notice, the original equation was $log_4color(blue)(x)=3$ , and since everything else is the same in these equations,

$color(blue)(x=64)$

Hope this helps!

If log_4 x =3log_4 x =3, then what is xx equal to?