WorksheetsLogarithm Properties
Total questions: 33
Worksheet time: 2hrs 12mins
Rewrite in exponential form:
log9 x = 2
9x = 2
2x = 9
29 = x
92 = x
Rewrite in exponential form.
log3 a = 5
5a = 3
log35 = log3a
a5 = 3
35 = a
Rewrite in Exponential Form:
log6 36 = 2
26 = 36
62 = 36
362 = 6
366 = 2
Rewrite in logarithmic form.
25 = 32
log25 = 32
log322 = 5
log232 = 5
log532 = 2
Rewrite logb (xn)
n⋅logb x
(logb x)n
xn⋅logb x
logb(xn)
Solve for x.
5x = 1
x = 0
x = -1
x = 2
x = 1
Rewrite in exponential form and solve for x.
log3 81 = x
x = 2
x = 3
x = 4
x = 5
Rewrite in exponential form and solve for x.
log5 (25) = x
x= 1/2
x= 2
x= 1
x= - 2
Rewrite in exponential form and then solve for x.
x = 2,097,152
x = 0.301
x = 1.322
x = 4.392
Expand using log properties.
log (2c2)
log 2 + 2⋅log c
log 2 ⋅ log c2
log 2 - 2⋅log c
log 2 + log c2
Expand using log properties
log (2 / 3)
log 2 + log 3
log 2 / log 3
log 2 - log 3
2/3 * log 1
Expand using log properties.
log (a2)
log a2
2 log a
log2 a
loga 2
Expand using log properties.
log (a2b4)
2⋅log(a) + 4⋅log(b)
4⋅log(a) + 2⋅log(b)
log(a2) + log(b4)
8(log(a) + log(b))
Expand using log properties.
logb(xy)
logbx + logby
logbx - logby
logbx ⋅ logby
logbx / logby
Expand using log properties.
logb(x/y)
logbx - logby
logbx + logby
logbx ⋅ logby
logbx / logby
6⋅log8(xyz)
log8(x) - log8(y) - 6⋅log8(z)
log8(x) + log8(y) - log8(z)
log8(x) + log8(y) + 6⋅log8(z)
Expand using log properties.
log(x²/y³)
log x² + log y³
2⋅log x + 3⋅log y
log x + log y
2⋅log x² +3⋅log y³
Condense using log properties.
log16 + log2 - log8
log4
log8
log10
log24
Expand using log properties.
log x + 5⋅log y
5⋅log x + 5⋅log y
5⋅log x - log y
log x - 5⋅log y
Expand using log properties.
6⋅log8v - 2⋅log8u
6⋅log8u - 2⋅log8v
3⋅log8u - 2⋅log8v
6⋅log8u + 2⋅log8v
Condense using log properties. Simplify completely.
log5 3 + log5 6 + log5 9
log5 69
log5 56
log5 162
log5 98
Condense using log properties. Simplify completely.
log 6 - log 3 + 2⋅log 7
log 98
log 78
log 56
log 45
Expand using log properties.
A
B
C
D
Condense using log properties. Simplify completely.
A
B
C
D
The common logarithm has what base?
0
10
1
2
To expand a logarithm that uses division, we use what operation?
Addition
Subtraction
Multiplication
Power
To expand a logarithm that uses multiplication, we use what operation?
Addition
Subtraction
Multiplication
Division
To condense a logarithm that uses addition, we use what operation?
Addition
Subtraction
Multiplication
Division
To condense a logarithm that uses subtraction, we use ______________ and simplify completely.
Addition
Subtraction
Multiplication
Division
What rule is shown?
Product Rule
Quotient Rule
Power Rule
Common Base Property
