3^x - 3^-x = 6.832 >> Calculator has solved this question for me...however I cannot understand method used....Can you help
+128408
I'm not sure what method your calculator may use, but here's an approach
3^x - 3^(-x) = 6.832
3^x - 1 / 3^x = 6.832 multiply through by 3^x
3^(2x) - 1 = 6.832 * 3^x rearrange as
(3^x)^2 - 6.832 * 3^x - 1 = 0
Let 3^x = y and we have that
y^2 - 6.832y - 1 = 0
Solving this by using the quadratic formula we have that
y ≈ -0.143362 or y ≈ 6.97536
Back-subsitutitng we have that
3^x ≈ -0.143362 or 3^x ≈ 6.97536
Since an exponenttial is never negative, reject the first solution....so....
3^x ≈ 6.97536 take the log of both sides
log 3^x ≈ log 6.97536 and we can write
x * log 3 ≈ log 6.97536 divide both sides by log 3
x ≈ log 6.97536 / log 3 ≈ 1.76803
