# Solve for x please -2e^-x = ??

#### alore

##### New member
Solve for x please -2e^-x = ??

I can't rearrange the equation to find an expression for x, Thanks in advance.

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#### Subhotosh Khan

##### Super Moderator
Staff member
Solve for x please -2e^-x = ??

I can't rearrange the equation to find an expression for x, Thanks in advance.
As posted this problem statement is incomplete.

Please post the complete problem - exactly.

#### Jomo

##### Elite Member
Solve for x please -2e^-x = ??

I can't rearrange the equation to find an expression for x, Thanks in advance.
-2e^-x = ??. Then e^(-x) = ??/-2 . Then -x = ln(-??/2). Then x = ln(-2/(??))

#### Peacock

##### New member
Here is one way with some brief explanations. When it says "Cross Multiplication" imagine that the right side of the equation is u/1.

#### HallsofIvy

##### Elite Member
I have always disliked the phrase "cross multiply"! I would think of that as two operations, "multiply both sides by $$\displaystyle e^x$$" and "divide both sides by u".

alore, think of this as "undoing" what has been done to x. The equation here is $$\displaystyle -2e^{-x}= ???$$. If you were given a value of x and asked to find ???, you would (1) multiply by -1 to get -x, (2) take the exponential to get $$\displaystyle e^{-x}$$, then (3) multiply by -2 to get $$\displaystyle -2e^{-x}$$.

To solve for x, do the opposite operations in the opposite order. The last thing you do in calculating $$\displaystyle -2e^{-x}$$ is multiply by -2 so to solve for x, the first thing you should do is divide by -2. Of course you have to do the same thing to both sides to keep the equation true. Dividing both sides by -2 gives $$\displaystyle \frac{-2e^{-x}}{-2}= e^{-x}= \frac{???}{-2}$$.

The opposite of the exponential is the logarithm. Taking the natural log of both sides is $$\displaystyle ln(e^{-x})= -x= ln(??/-2)$$. Finally the opposite of multiplying by -1 is the same as dividing by -1 (which happens to be the same as multiplying by -1): $$\displaystyle \frac{-x}{-1}= x= \frac{ln(??/-2)}{-1}= -ln(??/-1)$$.

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