Logarithms — Drills
Logarithms has 7 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 6 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Integer — A whole number, positive, negative, or zero.
- Base — The number being multiplied. In 53 the base is 5.
- Exponent — How many times the base is used as a factor. In 53 the exponent is 3.
- Zeros — The x values where y = 0.
- Logarithm — logb y is the exponent that turns b into y.
- Quotient — The answer to a division.
Evaluating
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Evaluate log4 64.
Worked answer
3
43=64
So the log is 3
Problem 2
Evaluate log5 125.
Worked answer
3
53=125
So the log is 3
Negatives
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Evaluate log3 19.
Worked answer
-2
3-2=19
Problem 2
Evaluate log5 125.
Worked answer
-2
5-2=125
Laws
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
If log x = 9 and log y = 7, find log (xy).
Worked answer
16
9+7=16
Problem 2
If log x = 2 and log y = 6, find log xy.
Worked answer
-4
2-6=-4
Powers
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
If log x = 5, find log x5.
Worked answer
25
5log x = 5(5) = 25
Problem 2
If log x = 6, find log x4.
Worked answer
24
4log x = 4(6) = 24
Solving
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve log3 x = 4.
Worked answer
81
x=34
=81
Problem 2
Solve log5 x = 3.
Worked answer
125
x=53
=125
Solvepow
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve 3x = 81.
Worked answer
4
81=34
So x=4
Problem 2
Solve 5x = 125.
Worked answer
3
125=53
So x=3
Domain
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For log(x-4) to be defined, what is the smallest integer x can be?
Worked answer
5
x-4>0
x>4, so the smallest integer is 5
Problem 2
For log(x-6) to be defined, what is the smallest integer x can be?
Worked answer
7
x-6>0
x>6, so the smallest integer is 7