How do you solve $36^(x-9)=6^(2x)$ ?

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Answer 1 · 2016-10-07T11:08:38

The equation has no solutions

We can solve exponential equation if the basis is the same, since

$a^x = a^y \iff x=y$

To bring your equation to this form, we simply need to observe that $36=6^2$ , and thus we have

$36^{x-9} = (6^2)^{x-9}$

Now use the rule $(a^b)^c = a^{b*c}$ to obtain

$(6^2)^{x-9} = 6^{2(x-9)}=6^{2x-18}$

So now the equation looks like

$6^{2x-18} = 6^{2x}$

which would be true only if

$2x-18=2x$ , which is clearly impossible

How do you solve 36^(x-9)=6^(2x)36^(x-9)=6^(2x)?