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

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alore

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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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alore said:
Solve for x please -2e^-x = ??

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

Please post the complete problem - exactly.
 
alore said:
Solve for x please -2e^-x = ??

I can't rearrange the equation to find an expression for x, Thanks in advance.
Click to expand...
-2e^-x = ??. Then e^(-x) = ??/-2 . Then -x = ln(-??/2). Then x = ln(-2/(??))
 
Exponents.jpg Here is one way with some brief explanations. When it says "Cross Multiplication" imagine that the right side of the equation is u/1.
 
I have always disliked the phrase "cross multiply"! I would think of that as two operations, "multiply both sides by ex\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 −2e−x=???\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 e−x\displaystyle e^{-x}, then (3) multiply by -2 to get −2e−x\displaystyle -2e^{-x}.

To solve for x, do the opposite operations in the opposite order. The last thing you do in calculating −2e−x\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 −2e−x−2=e−x=???−2\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 ln(e−x)=−x=ln(??/−2)\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): −x−1=x=ln(??/−2)−1=−ln(??/−1)\displaystyle \frac{-x}{-1}= x= \frac{ln(??/-2)}{-1}= -ln(??/-1).
 
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