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[@mostee77]

Excellent

[@superacademy247]

Thank you so much 😀

[@giuseppemalaguti435]

4t=3t^2..t=0(x=0)...t=4/3(x=16/9)

[@monroeclewis1973]

It’s interesting that when you get to 16x=9^x2 you can divide both sides by x, but then only get the x=16/9 solution. But if you form an equation and factor the way you did you get 2 solutions. Would you explain why you took your approach? Is there some rule or reason behind it?
Thanks,
MTC

[@tlubanski]

If you divide by x, you can only do that if x is not 0. That would eliminate 0 as a possible solution for x. The approach presented here is the correct one, because it does not exclude any possible solution by doing an operation on the equation.

[@monroeclewis1973]

@@tlubanski OK, thanks.

[@SidneiMV]

10^(2√x) = 10^(3x/2)
4√x = 3x
16x = 9x²
x(9x - 16) = 0
*x = 0* ∨ *x = 16/9*

[@l.w.paradis2108]

This was how I tried to do it in my head fast, and made a mistake the first time. (I bet you can guess where. :)
I see the reason for the longer approach.

[@SidneiMV]

@@l.w.paradis2108 well .. I don't know.. but .. maybe 16x = 9x² turned into 16 = 9x ..

[@michaeledwards2251]

Alternatively
4(root(x)) = 3x
4 = 3 (root(x))
4/3 = root(x) or x = 16/9.
x =0 implied by 10^0 = 1 giving 1 =1 by definition.