Expressing the Solution of 2^(2x+3) = 2^(x+1) + 3 as a + log2b: Complex Numbers

[musicmar]

Homework Statement

The solution of 2^(2x+3) = 2^(x+1) + 3 can be expressed in the form of: a + log₂b where a, b belong to the set of complex numbers.

The Attempt at a Solution

(2^3)(2^x)^2 = 2^(x+1) + 3

[8((2^x)^2)] - [2(2^x)] - 3 = 0

Solving the above quadratic for 2^x, I found that 2^x = 3/4 and -1/2. I can solve for x, but for simplicity's sake, I haven't yet.

From here, I need to put x into the above log form.

 

[gabbagabbahey]

Homework Statement

The solution of 2^(2x+3) = 2^(x+1) + 3 can be expressed in the form of: a + log₂b where a, b belong to the set of complex numbers.

The Attempt at a Solution

(2^3)(2^x)^2 = 2^(x+1) + 3

[8((2^x)^2)] - [2(2^x)] - 3 = 0

Solving the above quadratic for 2^x, I found that 2^x = 3/4 and -1/2. I can solve for x, but for simplicity's sake, I haven't yet.

From here, I need to put x into the above log form.

Looks good so far, but unless x is allowed to be a complex number, you can throw one of these solutions away...which one?

In order to get 'x' into the log form, just take log base 2 of both sides of your equation for 2^x... $\log_2(2^x)=x$