Use logarithms to solve the equation 4^(x+1)=5^(2x-3) , giving your answer correct to 3 significant figures.

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

Take log on both sides

`log (4^(x+1)) = log (5^(2x-3))`

`(x+1) log 4 = (2x-3)log5`

`0.6020(x+1) = (2x-3) 0.6990`

`x = 3.3912`

So the answer is x = 3.391

Sources:

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