First, let's apply some log rules to simplify our equation. We get
log3(x)=x from this.
We know Iff(x)=g(x),thenaf(x)=ag(x)
From this, we have 3log3(x)=3x
Which is the same as x=3x
There are NO SOLUTIONS to this equation.
Thanks! :)
Thanks, NotThat Smart !!!!
log2(log3x)=2log4(x)
To elaborate a little, we can use the change of base theorem to write
log ( logx / log 3 ) 2 log (x)
______________ = ________ { log 4 = log 2^2 = 2log 2 }
log 2 log 4
log ( log x / log 3 ) 2log (x)
______________ = _______
log 2 2log 2
log ( logx / log 3 ) = log (x)
This implies that
logx / log 3 = x
log x = xlog 3
log x = log 3^x
x = 3^x
Note here that the graphs of both functions never intersect
https://www.desmos.com/calculator/82kerdz2ip
So, like NotThatSmart, I don't find any solutions, either !!!