1 Answer

Mirla · Answer 1 · 2020-03-16T03:07:02+0000

Answer:

x = 10 or x = 100

Explanation:

The domain of the equation: x > 0.

We have:

$2+(\log x)^2=3\log x$

Substitute
$\log x=t$ :

2+t^2=3t subtract 3t from both sides

t^2-3t+2=0

t^2-2t-t+2=0

t(t-2)-1(t-2)=0

$(t-2)(t-1)=0\iff t-2=0\ \vee\ t-1=0$

t-2=0 add 2 to both sides

t=2

t-1=0 add 1 to both sides

t=1

We return to substitution:

$t=2\to\log x=2$

and

$t=1\to\log x=1$

Use

$\log_ab=c\iff a^c=b$

$\log a=\log_(10)a$

$\log_aa=1$

$\log x=2\iff x=10^2\to x=100\\\\\log x=1\to x=10$