SOLUTION: 2(4^x+1) = 1 Solve for x. thanks.

Question 92970: 2(4^x+1) = 1
Solve for x.
thanks.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Divide both sides by 2

Rewrite 4 as

Multiply the exponents

Distribute

Rewrite as

Now that we have the same base, we can set the exponents equal to each other

Add 2 to both sides

Combine like terms 2 and 1 on the right side to get 3

Now divide both sides by -2 to isolate and solve for x

Reduce

So our answer is

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Check:

Start with the given equation

Plug in

Combine like terms

Rewrite as

Evaluate to get

Take the square root of to get

Multiply. Since the two equations are equal, this verifies our answer.

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