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Linear equations and inequalities
Logs without a calculator
Log Properties
Exponential Applications
Equations
100
Write an equation of a line with slope of 5 and a y-intercept of 8
y = 5x + 8
100
log5(5) Read as Log base 5 of 5.
1
100
Expand and simplify: log(10x)
1+ log(x)
100
A town's population was 30 people. It is doubling every year. Write a function that describes the population of the town in x years.
f(x) = 30*(2)^x
100
2^(x-3)=8
{6}
200
Are the following parallel, perpendicular, or neither. y= 3x - 2 and 3y - x = 5
neither. The slopes are 3 and 1/3. To be parallel they must have the same slope. To be perpendicular they need opposite reciprocal. (change sign AND flip)
200
log5(25). Read as log base 5 of 25
2
200
Expand and simplify: log(x/10)
log(x) - 1
200
A retirement account is continuously decreasing by 4% a year. If the account had $1,000,000 when the person retired, write a function to describe the amount of money in the account x years since retirement.
f(x) = 1000000*e^(-.04x)
200
2^(x-3)=5. Write exact answer.
{log(5)/log(2) + 3} which is equivalent to {log2(5) + 3} read log base 2 of 5 plus 3. Note the 2 should be subscript, but I cannot do so with this program.
300
Identify the point and slope in the equation: y - 5 = 3(x + 2)
slope = 3, point = (-2, 5)
300
log5(1/25). Read as log base 5 of (1/25)
-2
300
Expand and simplify: log(100x^5)
2+ 5log(x)
300
A population of a town is continuously growing at a rate of 5%. It originally had 4,000 people. Write a function that represent the number of people in the town in x years.
f(x) = 4000*e^(0.05x)
300
e^(2x-1)=5. Write the exact answer.
{(ln(5)+1)/2} which equals {1/2ln(5) + 1/2}
400
Sally had 3 teddy bears in 1990. Every year she has added 2 to her collection. Write a function to describe the number of teddy bears x years since 1990.
f(x) = 2x + 3
400
log5(1). Read as log base 5 of 1
0
400
Expand and simplify: log(10(x+10)^2/y^3)
1 + 2log(x+10) - 3log(y)
400
A savings account is started by depositing 10,000. It is growing by 5% a year (compounded annually). Write the function.
f(x) = 10,000*(1.05)^x
400
log(3x-1)=2
{101/3}
500
Graph 3x - 2y > 6. The solution includes the description.
The line should be dashed. You need to solve for y, getting y < 3/2 x - 3 You graph by starting at (0,-3), and then moving up 3, right 3, to (2,0) and plot a point. Connect with a dashed line. Then shade below the line.
500
log5 (-5). Read as log base 5 of -5.
undefined
500
Condense to a single log: 4log(x)+3log(y)-2log(z)-8log(w)
log(x^4y^3/z^2w^8)
500
A bug population was at 15,000 when the bug bomb was deployed. 5% of the bugs are killed every hour. Write the function that describes the number of bugs left after x hours.
f(x) = 15,000*(0.95)^x
500
log(x) + log(x-3) = 1
{5} Note x not equal to -2, because not in domain/ makes input of logs negative.