Rewrite exp or log form
Expand or condense
Graph logarithms & characteristics
Solve
Applications with logs
100
Rewrite in exponential form
log7 343 = 3
73 = 3
100
Expand the logarithm
log x4a
4a log x
100
Graph the function and identify the domain and range.
f(x)= log3 x
Domain {x| x>0}, Range - all real numbers
100
Solve the equation
105x+6 = 10x-12
x=-9/2
100
An ant population began with 30 ants. From this point, the population continuously increased by 4% each hour. Based on this model, how many hours will it take the population to reach 100 ants. ONLY write an equation to set up to solve
100=30e.04t
200
Rewrite in log form
811/4 = 3
log81 3=1/4
200
Condense the logarithm
log 5 + log(x-4)
log (5x-20)
200
Graph the function and identify the asymptote and the increasing or decreasing interval
f(x)= log1/2 x
Asymptote: x=0;decreasing interval (0, oo)
200
Solve for x
log7(x+13) = log7(3-x)
x=-5
200
Only write the equation for this problem.
Sarah opened a savings account with a $725 deposit. This account earns 3.5% annual interest compounded twice each month. How long will it take her account to reach a balance of $2000 if there are no other deposits or withdrawals?
2000=725(1+.035/24)24t
300
Rewrite in log form
1315 = k
log13 k = 15
300
Expand the logarithm
log6(x5y2)
5log6 x + 2log6 y
300
graph the function and identify the end behavior
f(x) = - ln (x+5)
as x->-5, f(x)->- oo
as x -> oo, f(x)-> -oo
300
Solve for r
ln (r+1) + ln 2 = 7
r = 547.3165792
300
An ant population began with 30 ants. From this point, the population continuously increased by 4% each hour. Based on this model, how many hours will it take the population to reach 100 ants? Round your answer to tenths.
t = 30.1 hours
400
Rewrite in log form
17x = y
log17 y = x
400
Condense the logarithm
2/3 ln 64 - 2 ln 8
ln 1/4
400
graph the function and give the domain, range, and asymptote
f(x)= log1/3(x+1)-2
domain: {x|x>-1}. range: all real numbers, asymptote: x=-1
400
Solve for x
32x-5 =14
x= 3.7011
400
Students at a small college started coming down with a highly contagious virus. After t days, the number of people, P, who have been infected by the virus is modeled by the equation below. How long will it take the virus to spread to 500 people? round your answer to 2 decimal places. 
t= 7.95 days
500
Rewrite in exponential form
log100 1/10 = -1/2
100-1/2 = 1/10
500
expand the logarithm
ln (ac^2)/(bd^3)
ln a +2 ln c - ln b - 3 ln d
500
Graph the function and give the domain, range, asymptote, increasing or decreasing interval, end behavior
f(x) = log5(x+5)-1
D: {x|x>-5}, R: All real 3's, Asymptote: x=-5, increasing (-5, oo), end behavior: As x->-5, f(x)-> -oo, As x->oo, f(x)->oo
500
solve for K
82k+3 = 63k-1
k = 6.6015
500
Sarah opened a savings account with a $725 deposit. This account earns 3.5% annual interest compounded twice each month. How long will it take her account to reach a balance of $2000 if there are no other deposits or withdrawals? Round your answer to tenths.
t = 28.2 years