In her last two years in college, Marlene received $42,000 in loans. The first year, she received a loan that was $6,000 less than three times the amount of the second year's loan. Call the amount that Marlene received her first year f and the amount she received in her second year s.

First year = 30000

Second year = 12000

Step-by-step explanation:

Given

Represent first year with f and second year with s.

So, we have:

and

Required

Solve for f and S

Substitute 3s - 6000 for f in the first equation.

Collect Like Terms

Solve for s

Substitute 12000 for s in

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.