Question

0.5 log3 x=2 x = what

Answer 1

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

`(5 log_3 x)/(5) = (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

Answer 2

`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.