If $64^x-1=16^(x/2)$ , find $x$ ?

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Answer 1 · 2017-11-09T06:55:20

$x=3/2$

It is assumed here that we are given $64^(x-1)=16^(x/2)$ and not $64^x-1=16^(x/2)$

$64^(x-1)=16^(x/2)$

or $ln64^(x-1)=ln16^(x/2)$

or $(x-1)ln64=(x/2)ln16$

or $(x-1)(2/x)=ln16/ln64$

or $(x-1)1/x=ln16/(2ln64)$

or $1-1/x=ln2^4/(2ln2^6)$

or $-1/x=(4ln2)/(12ln2)-1$

or $-1/x=1/3-1=-2/3$

or $1/x=2/3$

i.e. $x=3/2$

If 64^x-1=16^(x/2)64^x-1=16^(x/2), find xx?