Which expression is equivalent to log18 – log(p + 2)?

log StartFraction p + 2 Over 18 EndFraction

log StartFraction 18 Over p + 2 EndFraction

log StartFraction 20 Over p EndFraction

log left-bracket 18 times (p + 2) right-bracket

log(18/(p+2))

log StartFraction 18 Over p + 2 EndFraction

Second option is the correct.

Step-by-step explanation:

There is a property of logarithms that when two logarithms are subtracting each other, we can make a single logarithm with the argument being the division of their arguments:

log(x) - log(y) = log(x/y)

So, with we have log18 – log(p + 2), we can rewrite as:

log18 – log(p + 2) = log(18/(p+2)), that is:

log StartFraction 18 Over p + 2 EndFraction

Second option is the correct.

Each one traveled 5.33kmEach one paid 20.8 PLN.

Explanation:

The translated information is:

The table lists the price lists of two taxi companies. The fare consists of a one-time initial payment and an additional fee depending on the length of the route traveled. Mr. Jan used the taxi "one", and Mr. Wojciech - the taxi "two". Both men covered the same distance and paid the same amount.

The mentioned table is:

                                   Taxi 1             Taxi 2

Initial payment           3.20 PLN       8.00 PLN

Price for 1km route    3.30 PLN       2.40 PLN

You can calculate how many kilometers both Mr. Jan and Mr. Wojciech traveled and how much they paid.

Solution

You can set a linear equation for each taxi.

The slope-intercept form of a linear equaion is;

     

Where m is the slope of the line and b is the y-intercept.

The slope is the rate of change of the dependent variable (y) per unit of the independent variable (x), and the y-intercept is the value of the dependent variable when the independent variable is zero.

In this case, you have, that the slopes are the price for 1km route and the y-intercepts are the initial payments. Thus, you have:

            Taxi 1                  Taxi 2

b          3.20 PLN            8.00 PLN

m         3.30 PLN/km     2.40 PLN/km

And the equations are:

Taxi 1                           Taxi 2

         

You can solve the system by equating the two equations:

       

Which means that they both traveled 5.33km

To calculate how much they paid you can use any of the two equations:

     

Which means they paid 20.8 PLN, each.