Question

solve for x.
3 + \log_{2}(2x) = 7
x = \square

Explanation:

Step1: Isolate the log term

Subtract 3 from both sides: $3 + \log_{2}(2x) - 3 = 7 - 3$
Simplify: $\log_{2}(2x) = 4$

Step2: Convert to exponential form

Using the definition of a logarithm ($\log_{b}(a) = c \implies b^c = a$), we get: $2^4 = 2x$

Step3: Solve for x

Calculate $2^4$: $16 = 2x$
Divide both sides by 2: $\frac{16}{2} = x$
Simplify: $x = 8$

Answer:

8