Question 639939
6^x-48*6^-x=2
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{{{6^x - 48*6^(-x) = 2}}}
Multiply by 6^x
{{{6^(2x) - 48 = 2*6^x}}}
Sub y for 6^x
{{{y^2 - 48 = 2y}}}
{{{y^2 - 2y - 48 = 0}}}
(y-8)*(y+6) = 0
y = -6 --> 6^x = -6 not allowed.
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y = 8 --> 6^x = 8
x*log(6) = log(8)
x = log(8)/log(6)
or {{{x = log(6,8)}}}
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x =~ 1.160558
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After doing this, I see I could have made it simpler:
{{{6^x - 48*6^(-x) = 2}}}
Sub y here
y - (48/y) = 2
etc