I'm supposed to solve using logrithims
(7)3/x = 5(2 - x) original equation
log7(7)3/x = log7(5)(2 - x) Take log (base 7) of each side.
(3/x)log77 = (2 - x)log75 Use logaun = n logau
(3/x) * 1 = (2 - x)log75 logaa = 1 because a1 = a
3/x = (2 - x)(log5/log7) change of base formula logax = log x/log a
3/x = (2 - x)(0.6989/0.8451) use calculator to find the values of log5 and log7
3/x = (2 - x)(0.827)
3 = (2 - x)(0.827)(x) Multiply by x on both sides
3/0.827 = (2 - x)(x) divide by 0.827 on both sides
3.628 = 2x - x2 distribute x on right side
Finally, it is a quadratic equation
x2 - 2x + 3.628 = 0
Here a = 1, b = -2 and c = 3.628
Use the quadratic formula and solve for x. You'll get two values of x as an answer. Just plug in the values of a, b, and c in the formula.
x = (-b ± √(b2 - 4ac))/2a
Good luck. If you need any help you can ask.