SOLUTION: Solve the exponential equation: 8^x - 3(8^-x) = 2 My answer key says it's x = log(3)/log(8) but I have no idea how to get there

Question 1061338: Solve the exponential equation:
8^x - 3(8^-x) = 2
My answer key says it's x = log(3)/log(8) but I have no idea how to get there
Answer by MathTherapy(10556) (Show Source): You can put this solution on YOUR website!

Solve the exponential equation:
8^x - 3(8^-x) = 2
My answer key says it's x = log(3)/log(8) but I have no idea how to get there

 =====>  =====>  =====> 

 ------- Multiplying by LCD, 



Let a = 

Then,  becomes:  

(a - 3)(a + 1) = 0

a - 3 = 0      OR         a + 1 = 0

a = 3          OR         a = - 1

Replacing "a" with 

       OR      

 ------ Converting 



 ------ Converting , but IGNORE this as LOG VALUE CANNOT be < 0 (negative) 

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