e^3x-7 x e^-2x =4e
First step I get e^1x-7 =4e
For the example in my book, the next step they divided by e. But I have no idea how to do this, or what involves?
You have to apply the indices rule: a^m /a^n= a^(m-n)
so e^(x-7)/e^1= e^(x-8). We then get: e^(x-8)=4 Use ln: x-8= ln4 so x=8+ln4
OK?
To solve the equation e^3x-7 * x * e^-2x = 4e, you can follow these steps:
Step 1: Simplify the equation.
e^3x-7 * x * e^-2x = 4e
Rewrite e^-2x as 1/e^2x.
e^3x-7 * x * (1/e^2x) = 4e
Step 2: Combine the terms with the same base.
Since e^3x-7 and 1/e^2x both have the base e, you can combine them by using the properties of exponents. Subtracting the exponents when dividing can be expressed as:
e^(3x-7-2x).
Therefore, the equation becomes:
e^(3x-7-2x) * x = 4e
Step 3: Simplify the exponent.
The exponent (3x-7-2x) can be simplified to (x-7).
So, the equation simplifies to:
e^(x-7) * x = 4e
Step 4: Divide by e.
To eliminate the exponential term e^(x-7) on the left side of the equation, you can divide both sides of the equation by e.
(e^(x-7) * x) / e = (4e) / e
This simplifies to:
x = 4
Therefore, the solution to the equation e^3x-7 * x * e^-2x = 4e is x = 4.
Note: When dividing an equation by a variable or expression containing variables (in this case, e), you can divide each term on both sides of the equation separately.
I hope this explanation helps you understand the process of solving the equation. Let me know if you need further clarification.