SOLUTION: {{{ 9^x+6^x=2^(2x+1) }}}

Question 560634:
Found 2 solutions by ankor@dixie-net.com, richard1234:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!

Just looking at this, you can see there is only one value for x that will make this work: x=0

1 + 1 = 2^1
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
x = 0 works, but we need to prove it is the only solution. Note that we can write the equation as

Dividing both sides by 4^x,

As you can see, the LHS is a strictly increasing function of x (bijective or one-to-one), so there can only be one value of x in which the LHS equals 2. We have already found it to be x=0.
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