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What are the solutions of the equation e^1-10x = 7?

Answer 1

Aurora Alvarado

If you meant # e^1 - 10x = 7 => x = (e-7)/10 =-0.42817 # (5dp)

If you meant # e^(1 - 10x) = 7 => x = (1-ln7)/10 = -0.09459 # (5dp)

There is an ambiguity in the way you have written the expression

Interpretation 1 : # \ \ e^1 - 10x = 7 #

# :. e - 10x = 7 #

# :. 10x = e-7 #

# :. x = (e-7)/10 # # \ \ \ \ \ \ \ = -0.4281718 ... # # \ \ \ \ \ \ \ = -0.42817 # (5dp)

Interpretation 2 : # \ \ e^(1 - 10x) = 7 #

# :. ln {e^(1 - 10x)} = ln7 #

# :. 1-10x = ln7 #

# :. 10x = 1-ln7 #

# :. x = (1-ln7)/10 # # \ \ \ \ \ \ \ = -0.09459101 ... # # \ \ \ \ \ \ \ = -0.09459 # (5dp)

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Answer 2

Aurora Alvarado

To find the solution for the equation ( e^{1-10x} = 7 ), you need to isolate ( x ). Here's the solution:

[ e^{1-10x} = 7 ] [ 1 - 10x = \ln(7) ] [ -10x = \ln(7) - 1 ] [ x = \frac{\ln(7) - 1}{-10} ]

So, the solution for the equation is ( x = \frac{\ln(7) - 1}{-10} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.