I think this is an exponential equation.
I can not figure out how to put the equation into the TI-84 to get the approximate form
3/5 ln(5x-1)+1 =1.4 subtract 1 from
sides and divide
by 3/5
lh(5x-1)=0.6667 Put in logarithm form
e^0.6667=5x-1 add 1 to both sides
e^0.6667=5x Divide by 5
e^0.6667 +1/5 exact form
I would leave the .66667 as 2/3, since your are talking about "exact" form
3/5 ln(5x-1)+1 =1.4
3/5 ln(5x-1) = .4
ln(5x-1) = 2/3
5x - 1 = e^(2/3)
5x = e^(2/3) + 1
x = (e^(2/3) + 1)/5 or (1/5)e^(2/3) + 1/5
your forgot to divide the first term by 5 and only divided 1 by 5
To solve the equation using a TI-84 calculator, you can follow these steps:
1. Clear the screen of any previous entries.
2. Press the "Y=" button to enter the equation screen.
3. Enter the expression on the left side of the equation: (3/5)*ln(5x-1)+1.
4. On the right side of the equation, subtract 1.4 from both sides to have 0 on the right side.
5. Now, your equation should look like (3/5)*ln(5x-1) = -0.4.
6. To isolate the natural logarithm term on the left side, divide both sides of the equation by (3/5) or multiply both sides by (5/3).
7. The equation should now be ln(5x-1) = -0.4*(5/3).
8. To eliminate the natural logarithm, convert the equation to exponential form. The base of the exponential function is "e," which is approximately 2.71828.
9. Apply the exponential function e^x to both sides of the equation. This will cancel out the natural logarithm on the left side, leaving you with 5x-1 = e^(-0.4*(5/3)).
10. Add 1 to both sides of the equation to isolate the variable. The equation becomes 5x = e^(-0.4*(5/3)) + 1.
11. Finally, divide both sides of the equation by 5 to solve for x. The equation now simplifies to x = (e^(-0.4*(5/3)) + 1)/5.
Using this equation, you can substitute the approximate value of e and evaluate the expression to get an approximate value for x.