Solve the equation. Put only integers or decimals for your answer.

Ask by Wheeler Olson. in the United States

Jan 14,2025

Question

Solve the equation. Put only integers or decimals for your answer. $$ \frac{2}{5}(2)^{x}=\frac{32}{5} $$

UpStudy AI · Accepted Answer

To solve the equation:

$$
\frac{2}{5} \cdot 2^{x} = \frac{32}{5}
$$

**Step 1:** Eliminate the fraction by multiplying both sides by 5:

$$
2 \cdot 2^{x} = 32
$$

**Step 2:** Simplify the left side:

$$
2^{x + 1} = 32
$$

**Step 3:** Recognize that $$32$$ is a power of 2:

$$
32 = 2^5
$$

**Step 4:** Set the exponents equal to each other:

$$
x + 1 = 5
$$

**Step 5:** Solve for $$x$$:

$$
x = 5 - 1
$$
$$
x = 4
$$

**Answer:**

4
$$ x = 4 $$

Solve the equation. Put only integers or decimals for your answer.