Logarithms Review

Converting

100

Write the following in logarithmic form

7^x =24

log_7 24=x

200

Write the following in logarithmic form:

8^2 =64

log_8 64=2

300

Write the following in exponential form:

ln5x=4

e^4 =5x

400

Write the following in logarithmic form:

e^(x+3) =60

ln60=x+3

500

Which is equivalent to the equation below?

log_2 18=x-1

2^(x-1)=18

Evaluating

100

Evaluate the log:

log_9 81

9^x =81

x=2

200

Evaluate the log:

log_36 6

36^x =6

x=1/2

300

Evaluate the log:

log_6 1

6^x =1

x=0

400

Approximate the value of the log to the thousandths place.

ln42

3.738

500

Approximate the following log to the ten-thousandths place:

log_5 84

5^x =84

x=2.753

Properties

100

Which property is listed below?

log_b (m*n)=log_bm+log_bn

Product Rule

200

Condense the expression:

log_b54 - log_b18

log_b (54/18)

log_b3

300

Expand the expression:

ln(2/a^3)^4

4*ln2 - 12*lna

400

Expand the expression:

log_5 (m^2n^3)^4

8*log_5m+12*logn

500

Condense the expression:

2*logx-(3*logy+logy)

log (x^2/y^4)

Solving Equations

100

Solve the following:

log_2(6x-15)=log_2(41-2x)

6x-15=41-2x

x=7

200

Solve the equation:

ln(p^2-p)=ln(6p+18)

p^2-p=6p+18

p= 9 & -2

300

Solve the following equation:

log_2(9m+2)=7

2^7 =9m+2

m=14

400

Solve the following equation:

3^(k-2) +7=82

log_3 75=k-2

(log_3 75)+2

5.9299

500

Solve the equation:

2*10^(5-y) +9=97

2*10^(5-y)=78

10^(5-y)=39

log_10 39=5-y

-log_10 39+5=y

y=3.4089

Growth/Decay/Interest

100

Which formula is this:

f(t)=a(1+r)^t

Growth

200

A bacteria culture begins with 500 bacteria and is growing exponentially. The number of bacteria after t hours is modeled by the function below. Find the amount of bacteria after 4 hours.

f(t)=500e^(0.9t)

18,299 bacteria

300

The population of a small town was 10,800 in 2002. Since then, it has decreased at a rate of 2.5% each year. Find the population of the town in 2020.

f(t)=10800(1-0.025)^18

6,847 people

400

Logan inherited $8,000 from his grandmother. He split his money evenly and placed the amounts into 2 accounts. How much money will he have after 5 years if one of the accounts earns 5.5% interest compounded annually?

f(t)=4000(1+(0.055/1))^(5*1)

$5,227.84

500

Logan inherited $8,000 from his grandmother. He split his money evenly and placed the amounts into 2 accounts. How much money will he have after 5 years if one of the accounts earns 7% interest compounded biweekly?

f(t)=4000(1+(0.07/26))^(5*26)

$5,673.60