3^x - 3^-x = 6.832 >> Calculator has solved this question for me...however I cannot understand method used....Can you help

Guest Jun 23, 2017

#1**+2 **

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

CPhill
Jun 23, 2017