If ${log}_{4} x = 3$ $log_4 x =3$ , then what is $x$ $x$ equal to?

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If ${log}_{4} x = 3$ $log_4 x =3$ , then what is $x$ $x$ equal to?

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Answer 1 · 2018-06-14T00:42:49

#x=3^4=81

Explanation:

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

Answer 2 · 2018-06-14T00:51:00

$x = 64$ $x=64$

Explanation:

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

${log}_{a} b = c$ $log_ab=c$

That this is equal to

$a^{c} = b$ $a^c=b$

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

$4^{3} = x \Rightarrow x = 64$ $4^3=x=>color(blue)(x=64)$

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

$a = {log}_{b} (b^{a})$ $a=log_b(b^a)$

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

$3 = {log}_{4} (4^{3})$ $3=log_4(4^3)$

$3 = {log}_{4} (64)$ $3=log_4color(blue)((64))$

Notice, the original equation was ${log}_{4} x = 3$ $log_4color(blue)(x)=3$ , and since everything else is the same in these equations,

$x = 64$ $color(blue)(x=64)$

Hope this helps!

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If ${log}_{4} x = 3$ $log_4 x =3$ , then what is $x$ $x$ equal to?

2 Answers

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