solve. we can use a calculator on this part...
2e^-x+4=21. how do i do this problem.
i know that you subtract 4, but what do you do after that?
2e^-x+4=21
2 e^-x = 17
e^-x = 17/2
1/e^x = 17/2
so
e^x = 2/17
take natural log of both sides
x = ln (2/17)
can you please show me how you got e^x=2/17. thanks
in general
a^-b = 1/a^b
To solve the equation 2e^-x + 4 = 21, you are correct that the first step is to subtract 4 from both sides of the equation:
2e^-x + 4 - 4 = 21 - 4
This simplifies to:
2e^-x = 17
Now, to isolate the exponential term e^-x, you need to divide both sides of the equation by 2:
(2e^-x) / 2 = 17 / 2
e^-x = 8.5
To get rid of the exponent and solve for x, you need to take the natural logarithm (ln) of both sides of the equation:
ln(e^-x) = ln(8.5)
Since the natural logarithm is the inverse function of the exponential function, they cancel out each other, leaving:
-x = ln(8.5)
Finally, to solve for x, you just need to multiply both sides of the equation by -1:
x = -ln(8.5)
To evaluate the solution numerically, you can use a calculator.
Note: When using a calculator, make sure it is set to calculate logarithms in the natural base (ln) and not the common base 10 (log).