Question

Please help me solve this

Answer 1

Answer: x = 1.186

Explanation:

To solve, we need to isolate the x variable.

Given:

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

Log both sides of the equation:

`Log(5^(2x-1))=Log(2^(x+2))`

Log power property:

`(2x-1)Log(5)=(x+2)Log(2)`

Distribute:

* Think of the Log(5) and Log(2) as a "regular number" that you can divide with, distribute with, etc

`2xLog(5)-Log(5)=xLog(2)+2Log(2)`

Add Log(5) to both sides of the equation and subtract xLog(2) from both sides of the equation:

`2xLog(5)-xLog(2)=2Log(2)+Log(5)`

Factor x from the terms on the left side of the equation:

`x(2Log(5)-Log(2))=2Log(2)+Log(5)`

Divide both sides of the equation by (2Log(5)-Log(2)):

`x= (2Log(2)+Log(5) )/(2Log(5)-Log(2))`

Compute:

x = 1.186