Converting
Write the following in logarithmic form
7^x =24
log_7 24=x
Evaluate the log:
log_9 81
9^x =81
x=2
Which property is listed below?
log_b (m*n)=log_bm+log_bn
Product Rule
Solve the following:
log_2(6x-15)=log_2(41-2x)
6x-15=41-2x
x=7
Which formula is this:
f(t)=a(1+r)^t
Growth
Write the following in logarithmic form:
8^2 =64
log_8 64=2
Evaluate the log:
log_36 6
36^x =6
x=1/2
Condense the expression:
log_b54 - log_b18
log_b (54/18)
log_b3
Solve the equation:
ln(p^2-p)=ln(6p+18)
p^2-p=6p+18
p= 9 & -2
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
Write the following in exponential form:
ln5x=4
e^4 =5x
Evaluate the log:
log_6 1
6^x =1
x=0
Expand the expression:
ln(2/a^3)^4
4*ln2 - 12*lna
Solve the following equation:
log_2(9m+2)=7
2^7 =9m+2
m=14
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
Write the following in logarithmic form:
e^(x+3) =60
ln60=x+3
Approximate the value of the log to the thousandths place.
ln42
3.738
Expand the expression:
log_5 (m^2n^3)^4
8*log_5m+12*logn
Solve the following equation:
3^(k-2) +7=82
log_3 75=k-2
(log_3 75)+2
5.9299
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
Which is equivalent to the equation below?
log_2 18=x-1
2^(x-1)=18
Approximate the following log to the ten-thousandths place:
log_5 84
5^x =84
x=2.753
Condense the expression:
2*logx-(3*logy+logy)
log (x^2/y^4)
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
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