Final answer:
To solve the equation lne^(3x-100)=4760, apply logarithmic and exponential properties to isolate x and find that the price of one cash register is $1620.
Step-by-step explanation:
The equation given is lne^(3x-100)=4760. To solve for x, the variable representing the price of one cash register, we'll use properties of logarithms and exponents. The natural logarithm function ln is the inverse of the exponential function with base e. Applying this property, we can simplify the equation as follows:
- lne^(3x-100)=4760
- 3x - 100 = 4760, because ln(e^y) = y for any y
- 3x = 4860, by adding 100 to both sides of the equation
- x = 4860 / 3, by dividing both sides by 3
- x = 1620, which is the price of one cash register
Therefore, x, the price of one cash register, is $1620.