Respuesta :

gmany
[tex]0.5\log_3x=2[/tex]

[tex]Domain:x\in\mathbb{R^+}[/tex]

[tex]0.5\log_3x=2\ \ \ |\cdot2\\\\\log_3x=4[/tex]

[tex]Use\ the\ de finition\ of\ the\ logarithm:\\\\\log_ab=c\iff a^c=b[/tex]

[tex]Therefore\ we\ have:\\\\\log_3x=4\iff3^4=x\to x=81[/tex]

Answer: C. 81.
Here is another method:
[tex]0.5 log_3 (x) = 2[/tex]

Multiply both sides by 10 to get rid of the decimal:
[tex]10 * 0.5 log_3 (x) = 10 * 2[/tex]
[tex]5 log_3 (x) = 20[/tex]

Divide 5 out
[tex]\frac{5 log_3 x}{5} = \frac{20}{5}[/tex]
[tex]log_3 x = 4[/tex]

Now use the log rule [tex]a = log_b b^a[/tex]
[tex]4 = log_3 (3^4) = log_3 (81)[/tex]

Since we have the same base
[tex]log_3 (x) = log_3 (81)[/tex]
x = 81