Graphing or Find the inverse
Write as a log/ exponential or calculate
Log Properties: Fully expand or condense
Solve the following equations
Growth and Decay
100
Find the inverse:
f(x)= log_2(x-6)
y=2^x+6
100
Write as a logarithm:
3^(x+1)=81
x=log_3(81)-1
100
Expand:
ln(2/x)
=ln(2)-ln(x)
100
log_2(2x-1)=log_2(3x+4)
x=-5
100
The rabbit population is decreasing at a rate of 4.5% per year. If the current population is 10,000 when will the rabbit population be 4,000?
It will take about 20 years for the population to reach 4,000 rabbits.
200
Find the inverse:
f(x)= e^(x+1)
f^-1(x)=ln(x)-1
200
Write as a logarithm:
e^(3x)=12
x= ln(12)/3
200
Condense:
2ln(x)-ln(y)
=ln(x^2/y)
200
log_3(x+3)=2
x=6
200
You invest $3,000 in an account with an interest rate of 1.5%. How many years till you triple your money?
It will take 74 years until I triple my money.
300
Find the inverse:
f(x)= log(x-3)
y=10^x+3
300
ln(x+2)=3
x=e^3-2
300
log_2(x^5y)
Expanding:
5log_2(x) + log_2(y)
300
log_4(x-4)=2
x=20
300
$600 is invested in an account that compounds continuously. What rate do you need to have $1,200 in your account in 5 years.
I would need a rate of 13.9% to have $1,200 in my account in 5 years.
400
Graph the following equation:
f(x)=3log_2(x-1)+2
400
Use your calculator to approximate:
log_4(21)
round to 3 decimal places
=log21/log4
=2.196
400
3log(x)+log(y)
Condense:
log(x^3y)
400
Round answer to 3 decimal places
2^x-2=18
x=4.322
400
$500 is invested in an account that compounds continuously. What rate do you need to double your money in 10 years?
I need a rate of 6.9% to double my money in 10 years.
500
Graph the following equation:
f(x)=2log_(1/3)(x+2)-1
500
Use your calculator to approximate
log_3(15)
round to the 3rd decimal place
=log15/log3
=2.465
500
2log_3(x)+log_3(y)-log_3(z)
Condense:
log_3((x^2y)/z)
500
3^(x+1)-2=0
x=-0.369
500
Gaby started a youtube channel with 100 subscribers. Every month the number of subscribers increases by 5%. After how many months will Gaby have 1,550 subscribers?
Gaby will have 1,550 subscribers after 672 months.