Problem: Use Common or Natural Logarithims to solve the exponential equations symboliclly.
2e^7x+4=4
(Round to four decimal places)
I tried solving this way
2e/2^7x+4=4/2
e^7x+4=2
ln e^7x+4=ln 2
7x+4=ln 2
7x+4-4=ln 2-4
7x=ln 2-4
7x/7=ln 2-4/7
x=ln 2-4/7
then I at a lose at this point.
What step should I perform next.
I know I'm suppose to use the calculator for the estimated solution, but I'm not coming up with the correct answer. Help!!!
2e^7x +4=4
2e^7x=0
e^7x=0
ln1=0
so 7x=1
x=1/7
v.easy
Yes this would be very simple, except this is a logarithim equation. The answer you gave isn't correct either.
the e actually represect ln.
Lee, the solution that John gave you is correct according to the way you typed the question.
I have a feeling you meant to type
2e^(7x+4) = 4
if so, then
e^(7x+4) = 2
take ln of both sides
ln(e^(7x+4)) = ln2
(7x+4)lne = ln2 , but lne = 1
7x+4 = ln2
7x = ln2 - 4
x = (ln2 - 4)/7 or appr. - .4724
you are correct. I understand it now. You are such a fantastic help :)
To solve the equation 2e^(7x+4) = 4, you made some mistakes in your calculations. Let's break down the solution step-by-step:
1. Divide both sides of the equation by 2:
(2e^(7x+4))/2 = 4/2
e^(7x+4) = 2
2. Take the natural logarithm (ln) of both sides:
ln(e^(7x+4)) = ln(2)
7x+4 = ln(2)
3. Subtract 4 from both sides:
7x+4-4 = ln(2) - 4
7x = ln(2) - 4
So far, your calculations are correct up to this point. Now, to solve for x, we need to isolate it.
4. Divide both sides of the equation by 7:
7x/7 = (ln(2) - 4)/7
x = (ln(2) - 4)/7
To find the approximate value of x, you can use a calculator. Just make sure to input the values correctly.
Now, let's calculate it step-by-step:
1. Calculate the value of ln(2) - 4:
ln(2) ≈ 0.6931471806
ln(2) - 4 ≈ -3.3068528194
2. Divide the result by 7:
(-3.3068528194) / 7 ≈ -0.4724075456
Rounded to four decimal places, the approximate value of x is:
x ≈ -0.4724
Remember to double-check your calculations and the input on your calculator to ensure accuracy.