# 2e^(4x^2)=3

how do i solve for x. do i use the ln methode because i don't know how to do that. by calculator, i got x=.168 but i don't know how to show my work. please help me solve for x.

Take natural logs of both sides.

ln 2 + 4 x^2 = ln 3

4 x^2 = ln (3/2) = 0.40547

x^2 = 0.10137

x = (+ or -) 0.31838...

5x-12=2x-21

## To solve the equation 5x-12=2x-21, you can use the method of isolating the variable on one side of the equation.

1. Start by subtracting 2x from both sides of the equation to eliminate the 2x term on the right side:

5x - 2x - 12 = 2x - 2x - 21

Simplify it:

3x - 12 = -21

2. Next, add 12 to both sides of the equation to move the constant term to the right side:

3x - 12 + 12 = -21 + 12

Simplify it:

3x = -9

3. Finally, divide both sides of the equation by 3 to isolate the variable x:

(3x)/3 = (-9)/3

Simplify it:

x = -3

Therefore, the solution to the equation 5x-12=2x-21 is x = -3.