Final answer:
To solve 3ʳ - 1 = 4, add 1 to both sides to get 3ʳ = 5, then take the natural logarithm of both sides to isolate x and get x = ln(5)/ln(3). The calculation gives approximately 1.46497, which rounds to 1.46, making option (a) the correct answer.
Step-by-step explanation:
To solve the equation 3ʳ - 1 = 4, you need to isolate the exponent by first adding 1 to both sides of the equation, which gives you 3ʳ = 5. Next, you can solve for x by taking the logarithm of both sides. You would typically use the natural logarithm or the logarithm base 3, but for simplicity here, let's use the natural logarithm (ln). The equation then becomes ln(3ʳ) = ln(5). Since the properties of logarithms state that ln(aʹ) = b * ln(a), you can rewrite the equation as x * ln(3) = ln(5). Now, divide both sides by ln(3) to solve for x, yielding x = ln(5)/ln(3).
Using a calculator, you find that ln(5)/ln(3) is approximately 1.46497, which rounds to 1.46. Therefore, the correct answer from the options provided is (a) 1.46.