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AP Precalculus Log Exponential

Total questions: 15

Worksheet time: 15mins

Name
Class
Date
1.

Write logb(x/y) as two logs

a)

logbx-logby

b)

logbx+logby

c)

logbx*logby

d)

logbx/logby

2.

Use multiple log properties to write as a single log:
log2x -  5log2y

a)

log2(x/y5)

b)

log2(xy5)

c)

log2(x/y)5

d)

log2(x/5y)

3.

Rewrite logb(xn)

a)

nlogbx

b)

(logbx)n

c)

xnlogbx

d)

logb(xn)

4.

Change to Exponential Form:
log636 = 2

a)

26=36

b)

62=36

c)

362=6

d)

366=2

5.

Expand the following logarithm: 
log2 5x.

a)

log2 5 - log2 x 

b)

log2 5 + log2 x 

c)

2log 5 + 2log x

d)

log5 2 + logx 2

6.

Write as a single log: log 12 + 2 log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x2)

7.

When you have two log expressions separated by a minus sign (-), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

8.

Solve:

log (x - 1) - log (x - 2) = log 5

a)

7

b)

4/9

c)

9/4

d)

1/7

9.

Use multiple log properties to write as a sum or difference of two logs: log(4x3

a)

log 4 + 3log x

b)

3log 4 + 3log x

c)

3log 4 + log x

d)

log 12 + log x

10.

Solve for x:  log6x + log6(x-5) = 2

a)

√7

b)

9

c)

4

d)

none of these

11.

ln(x+8) - ln (8) = 3

a)

152.68

b)

188.77

c)

4.24

d)

8.01

12.

log9(10)-log9(x-3) =log9(72)

a)

81/16

b)

113/36

c)

No Solution

d)

92/15

13.

log9(x)+log9(x+2)=log9(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

14.

log5x - log5(x+4)=log538

a)

-152/37, -8

b)

1/2

c)

-152/37

d)

No Solution

15.

log7+log(x2-4)=log35

a)

-1

b)

-2

c)

-3

d)

-4