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!