Need help with logarithms
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Need help with logarithms

[From: ] [author: ] [Date: 11-08-31] [Hit: ]
x * ln(2) = ln(4 + sqrt(15)) ,x = ln(4 + sqrt(15)) / ln(2),......
I know you need to use logarithms to solve the equation, but i get lost or am missing a step if anyone can walk me through it, not necessarily solve, that would be great!

2^x + 2^-x = 8

-
2^x + 2^(-x) = 8
2^x + 1/(2^x) = 8

Here's where it gets fun. Let 2^x = t

t + 1/t = 8

Multiply everything by t

t^2 + 1 = 8t
t^2 - 8t + 1 = 0
t = (8 +/- sqrt(64 - 4)) / 2
t = (8 +/- 2 * sqrt(15)) / 2
t = 4 +/- sqrt(15)
2^x = 4 +/- sqrt(15)
x * ln(2) = ln(4 + sqrt(15)) , ln(4 - sqrt(15))
x = ln(4 + sqrt(15)) / ln(2) , ln(4 - sqrt(15)) / ln(2)
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