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Question 48879: Solve for x, computing the answer to 4 significant digits
e^x=0.349
Answer by Born2TeachMath(20)   (Show Source):
You can put this solution on YOUR website! Like all algebraic equations, the idea is to get the "x" variable by itself on one side of the equation, and the answer on the other. To do this, we use mathematical operations: addition to get rid of subtraction, division to get rid of multiplication, etc. Almost every mathematical function has a function that "undoes" it, just like square roots "undo" squaring.
The exponential function e^x is just another function, although a very confusing function for most beginners. The function that "undoes" "e" is the natural logarithmic function "ln". Another similar set of functions are the "10^x" function and the "log" function. As you can see on most calculators, these sets of buttons are located with eachother, usually one is the "shift" or "2nd" of the other. This is not a coincidence!
Therefore, to get rid of the "e" on the left side of the equation, we apply the "ln" function to both sides of the equation:
ln(e^x) = ln(0.349)
Since the "ln" and the "e" are inverse functions (similar to square rooting something squared) they cancel eachother out, and we're left with:
x = ln(0.349)
This is the exact answer form to your question.
Your question asked for the decimal approximation to 4 significant figures, so to evaluate this, we simply grab a calculator and type "ln 0.349" on the calculator, and get an answer of -1.052683357.
So to 4 significant digits, the answer is: -1.053.
Here's your work:
e^x = 0.349
ln(e^x) = ln(0.349)
x = -1.052683357
x = -1.503 (4 sig figs)
You can check the by trying e^-1.053 on your calculator. The answer should be very close to 0.349.
That's how "e" and "ln" are related. They're just inverse functions, just like adding and subtraction, multiplication and division.
Good luck...
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