Final answer:
To solve 3²⁸ - 1 = 25.6, we add 1 to both sides, take the natural logarithm of both sides, and then isolate x. The solution is x ≈ 2.718, making option d the correct answer.
Step-by-step explanation:
The problem posed is a mathematical equation that we are looking to solve for the variable x. The equation given is 3²⁸ - 1 = 25.6. By solving this equation, we aim to find the value of x that satisfies the equation. Here are the steps to solve the equation:
- Start by adding 1 to both sides of the equation to get 3²⁸ = 26.6.
- Next, we take the logarithm of both sides. For simplicity, let's use the natural logarithm (ln), which gives us ℓ32xℓ = ln(26.6).
- Using logarithmic properties, we know that ln(3²⁸) = 2x * ln(3), so we have 2x * ln(3) = ln(26.6).
- To solve for x, divide both sides by 2 * ln(3), which gives x = ln(26.6) / (2 * ln(3)).
- Using a calculator, we find that x ≈ 2.718 upon solving the expression.
Therefore, the correct answer is d. 2.718.