2log 2/2(x + 3) = 1 + log z(x + 3)

To solve the equation \( 2\log\left(\frac{2}{2}\right)(x + 3) = 1 + \log(z(x + 3)) \), we can simplify and rearrange it step by step.

Step 1: Simplify the left side

Firstly, note that \( \frac{2}{2} = 1 \), so: \[ \log\left(1\right) = 0. \] Therefore, the left side becomes: \[ 2 \cdot 0 = 0. \]

So the original equation simplifies to:

\[ 0 = 1 + \log(z(x + 3)). \]

Step 2: Rearranging the equation

Subtract 1 from both sides: \[ -1 = \log(z(x + 3)). \]

Step 3: Convert logarithmic form to exponential form

Using the property of logarithms, we can express this logarithmic equation in exponential form: \[ z(x + 3) = 10^{-1}. \] Thus: \[ z(x + 3) = 0.1. \]

Step 4: Solve for \( z \)

Now, we can express \( z \) in terms of \( x \): \[ z = \frac{0.1}{x + 3}. \]

Conclusion

The solution to the equation is: \[ z = \frac{0.1}{x + 3}. \] This expresses \( z \) as a function of \( x \). If you need specific values for \( z \) or \( x \), you would need additional constraints or equations.

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