To solve the equation \(2^{(x+5)} = 4\), we can follow these steps:

### Step 1: Simplify the Right Side
We know that \(4\) can be expressed as a power of \(2\):
\[
4 = 2^2
\]

So, rewrite the equation as:
\[
2^{(x+5)} = 2^2
\]

### Step 2: Set the Exponents Equal to Each Other
Since the bases are the same (both are \(2\)), we can set the exponents equal to each other:
\[
x + 5 = 2
\]

### Step 3: Solve for \(x\)
Now, isolate \(x\) by subtracting \(5\) from both sides:
\[
x = 2 - 5
\]

\[
x = -3
\]

So, the solution is \(x = -3\).

Would you like more details or have any questions?

Here are some related questions to explore further:

1. How would you solve \(3^{(x+2)} = 9\)?
2. What is the general method to solve exponential equations of the form \(a^{(bx+c)} = d\)?
3. How do you solve \(2^{(x+3)} = 8\)?
4. How can logarithms be used to solve \(10^{(2x+1)} = 1000\)?
5. How do you graph the function \(y = 2^{(x+5)}\) and find its intersections with \(y = 4\)?

**Tip:** When solving exponential equations, express all terms with the same base to simplify the process of equating the exponents!

Learn how to solve the exponential equation 2^(x+5) = 4 with a clear step-by-step solution. This problem explores the algebraic method of equating exponents by expressing terms with the same base. Suitable for students in Grades 8-10.

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