Logarithms and Finance

Converting Log and Exponential Form

100

Convert to Exponential Form:

log_2(8)=x

2^x=8

200

Convert to Logarithmic Form:

4^y=x

log_4(x)=y

300

Convert to Exponential Form:

log_(x-1)(4)=2y

(x-1)^(2y)=4

Solving Log Equations with Log Properties

100

Solve for x:

log_3(x-3)=log_3(55)

x=58

200

Solve for x:

log_5(x+6)=log_5(3x)

x=3

300

Solve for x:

2ln(2)+ln(x)=ln(x+12)

x=4

Expanding/Condensing Logarithms

100

Condense the Logarithms:

log_3(2x)-log_3(5y)

log_3((2x)/(5y))

200

Completely Expand the Logarithm:

log((2x)/y)

log(2)+log(x)-log(y)

300

Condense the Logarithms:

2ln(3)-2ln(x)+4ln(y)

ln((9y^4)/x^2)

Solving Exponential Equations with Logs

100

Solve using Logarithms. Round the answer to the hundredth if necessary:

6^x=90

x=2.51

200

Solve Using Logarithms. Round the answer to the hundredth if necessary:

3^(7x)=108

x=0.61

300

Solve by Converting:

log_4(x)=5

x=1024

Mathematics of Finance

100

June made an initial deposit of $5700 in an account for her son. Assuming an interest rate of 6% compounded
quarterly, how much will the account be worth in 15 years?

$13,926.35

200

If Bob deposits $5000 at the end of each year for 15 years in an account paying 6% interest compounded
annually, find the amount he will have on deposit.

 $116,379.85

300

In order to purchase a home, a family borrows $45,000 at an annual interest rate of 13%, to be paid back over a 30-year period in equal monthly payments. What is their monthly payment?

$497.79