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To solve the equation 7*4^(x-1) + 4^(x+1) = 23, we can simplify it by using the properties of exponents.

Let's start by rewriting 4^(x-1) as (4^x)/(4^1) = 4^x/4.

Now, we can substitute this expression back into the equation:

7*(4^x/4) + 4^(x+1) = 23.

Next, we can simplify the equation further by multiplying both sides by 4 to get rid of the fraction:

7*4^x + 4^(x+1)*4 = 92.

Now, we can rewrite 4^(x+1)*4 as 4^(x+2):

7*4^x + 4^(x+2) = 92.

Since both terms have the same base (4), we can combine them:

7*4^x + 16*4^x = 92.

Now, we can combine like terms:

23*4^x = 92.

Divide both sides by 23:

4^x = 4.

Since 4 can be written as 2^2, we can rewrite the equation as:

(2^2)^x = 2^2.

Using the property of exponents, we can simplify further:

2^(2x) = 2^2.

Since the bases are the same, we can equate the exponents:

2x = 2.

Divide both sides by 2:

x = 1.

Therefore, the solution to the equation 7*4^(x-1) + 4^(x+1) = 23 is x = 1.