Final answer:
To solve the equation lne³ˣ⁻¹⁰⁰ = 4760 for x, you first simplify to 3x - 100 = ln(4760), then solve for x, ensuring to match the significant figures of the original data which are in the ones place.
Step-by-step explanation:
The equation presented is lne³ˣ⁻¹⁰⁰ = 4760. To solve this equation, we need to apply the properties of logarithms and exponential functions. The base of the natural logarithm 'ln' is 'e', so the equation can be simplified by using the property where 'ln' and 'e' cancel each other out. We then obtain e³ˣ⁻¹⁰⁰ = 4760. To isolate the variable x, we take the natural logarithm of both sides which yields 3x - 100 = ln(4760). Solving for x, we get x = (ln(4760) + 100) / 3. After calculating the value, we must consider the significant figures. The final answer is provided in the ones place because the initial values mentioned have their most significant figures in the ones place.