Question

70 points! Help! I'm new to this concept. Please help me find the solution set of this equation. Infinite thanks in advance for the solver :D

Answer 1

{log(x )}² + log(x²) ={ log(2)}² -1

{ log(x ) }² +2 logx = { log2}² - 1

let logx = P

P² + 2P ={ log(2) }² -1

P² + 2P = {log(2) }² -1

P² +2P + 1 = { log(2) }²

( P +1)² = { log(2) }²

P + 1 = ± log2

P =- 1 ± log2

P = - log10 ± log2 = (log2 - log10 ) , (- log10 - log2)

P = log1/5 , log1/20

now ,
P = logx = log1/5 , log1 20

so,

x =1/ 5 , 1 /20

Answer 2

(log(x))²+log(x²)+1=(log(2))²
(log(x))²+2log(x)+1=(log(2))²
Now LHS is a quadratic equation in terms of log(x) and it is of the form (a+b)²=a²+2ab+b²
So, (log(x)+1)²=(log(2))²
⇒ logx+1=log2
 logx=log2-1
 logx=log2-log10
 logx=log2/10
logx=log1/5
 x=1/5
HOPE THIS HELPS...