The equation you've written is:

\[
(2)^3x + 2 = 256
\]

This can be interpreted as:

\[
(2^{3x}) + 2 = 256
\]

Let's solve this step by step.

### Step 1: Subtract 2 from both sides.
\[
2^{3x} = 256 - 2
\]
\[
2^{3x} = 254
\]

### Step 2: Check if 254 can be expressed as a power of 2.
254 is not a power of 2. Hence, the equation does not have an exact solution involving integer powers of 2.

If you want to find an approximate solution, we can take the natural logarithm of both sides and solve for \( x \).

Would you like me to proceed with finding an approximate solution using logarithms, or is there something you'd like to clarify?

---

Here are some questions you might explore further:

1. What are logarithms and how do they help in solving equations?
2. What is the significance of powers of 2 in mathematical equations?
3. How do we solve equations involving exponents with non-integer results?
4. Can every number be expressed as a power of 2?
5. How would the solution change if the exponent base was different?

**Tip**: When solving exponential equations, logarithms are often useful if you can't express the number on both sides as powers of the same base.

Discover how to solve the exponential equation (2)^3x + 2 = 256. This problem involves exponent properties and logarithms. Learn step-by-step how to handle exponents and why certain numbers can or cannot be expressed as powers of 2. Suitable for high school students, Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation