Question

0.5 log3 x=2 x = what

Answer 1

$0.5\log_3x=2$

$Domain:x\in\mathbb{R^+}$

$0.5\log_3x=2\ \ \ |\cdot2\\\\\log_3x=4$

$Use\ the\ de finition\ of\ the\ logarithm:\\\\\log_ab=c\iff a^c=b$

$Therefore\ we\ have:\\\\\log_3x=4\iff3^4=x\to x=81$

Answer: C. 81.

Answer 2

Here is another method:
$0.5 log_3 (x) = 2$

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

Divide 5 out
$\frac{5 log_3 x}{5} = \frac{20}{5}$
$log_3 x = 4$

Now use the log rule $a = log_b b^a$
$4 = log_3 (3^4) = log_3 (81)$

Since we have the same base
$log_3 (x) = log_3 (81)$
x = 81