+130553 0=4(e^(2x)) - e^(-x) rearrange
e^(-x) = 4e^2x (1)
1 /e^(x) = 4e^(2x) multilpy both sides by e^x and divide both sides by 4
1/4 = e^(3x) take the Ln of both sides
Ln(1/4) = Ln e^(3x) and, by a log property, we can write
Ln(1/4) = 3x Lne and Lne = 1 ....so we have
Ln(1/4) = 3x divide both sides by 3
Ln(1/4)/3 = x = about -0.462
Here's the graph of both sides of (1) above showing the approximate solution.......
https://www.desmos.com/calculator/u8u7qz89kc
+130553 0=4(e^(2x)) - e^(-x) rearrange
e^(-x) = 4e^2x (1)
1 /e^(x) = 4e^(2x) multilpy both sides by e^x and divide both sides by 4
1/4 = e^(3x) take the Ln of both sides
Ln(1/4) = Ln e^(3x) and, by a log property, we can write
Ln(1/4) = 3x Lne and Lne = 1 ....so we have
Ln(1/4) = 3x divide both sides by 3
Ln(1/4)/3 = x = about -0.462
Here's the graph of both sides of (1) above showing the approximate solution.......
https://www.desmos.com/calculator/u8u7qz89kc
