If a satisfies the equation log22x+log33x=log44x2, then the value of loga3=....
Explanation
Recall some logarithm concepts
logab=logba1
logabc=logab+logac
And also logambn=mn⋅logab.
Let's simplify the logarithm form
log22x+log33x=log44x2
log22+log2x+log33+log3x=log44+log4x2
1+log2x+1+log3x=1+log22x2
1+log2x+log3x=22⋅log2x
log3x=−1
logx3=−11=−1
Therefore the solution is x=a so
loga3=−1