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Solve for x: 3^(2x-1)=5^(x)

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The equation `3^(2x-1)=5^(x)` has to be solved for x.

`3^(2x-1)=5^(x)`

take the log of both the side

`log(3^(2x - 1)) = log(5^x)`

Use the property of logarithm log a^b = b*log a

=> `(2x - 1)(log 3) = x*log 5`

=> `x*2*log 3 - log 3 = x*log 5`

=> `x(2*log 3 - log 5) = log 3`

=> `x = (log 3)/(2*log 3 - log 5)`

=> `x = (log 3)/(log(9/5))`

=> `x~~1.869`

The solution of the equation is approximately x = 1.869

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