# CONVERTING BETWEEN LOGARITHMIC AND EXPONENTIAL FORMS WORKSHEET

Converting between Logarithmic and Exponential Forms Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on converting between logarithmic and exponential forms.

Before look at the worksheet, if you would like to learn how to do conversions between logarithmic and exponential forms,

## Converting between Logarithmic and Exponential Forms Worksheet - Problems

Problem 1 :

Convert the following into exponential form :

log464  =  3

Problem 2 :

Convert the following into exponential form :

log5(1/25)  =  -2

Problem 3 :

Convert the following into exponential form :

log√39  =  4

Problem 4 :

Convert the following into exponential form :

log100.1 =  -1

Problem 5 :

Convert the following into exponential form :

log0.58  =  -3

Problem 6 :

Convert the following into logarithmic form :

1/1296  =  6-4

Problem 7 :

Convert the following into logarithmic form :

(13)-1  =  1/13

Problem 8 :

Convert the following into logarithmic form :

8-2/3  =  1/4

Problem 9 :

Convert the following into logarithmic form :

10-1  =  0.1

Problem 10 :

Solve for x :

log1/5x  =  3

Problem 11 :

Solve for x :

logx125√5  =  7

Problem 12 :

Solve for x :

logx0.001  =  -3

Problem 13 :

Solve for x :

log5(5log3x)  =  2

Problem 14 :

Solve for x :

x + 2log279  =  0

Problem 15 :

Solve for x :

log3x + log9x + log81x  =  7/4 ## Converting between Logarithmic and Exponential Forms Worksheet - Solutions

Problem 1 :

Convert the following into exponential form :

log464  =  3

Solution :

64  =  43

Problem 2 :

Convert the following into exponential form :

log5(1/25)  =  -2

Solution :

1/25  =  5-2

Problem 3 :

Convert the following into exponential form :

log√39  =  4

Solution :

9  =  (√3)4

Problem 4 :

Convert the following into exponential form :

log100.1 =  -1

Solution :

0.1  =  10-1

Problem 5 :

Convert the following into exponential form :

log0.58  =  -3

Solution :

8  =  0.5-3

Problem 6 :

Convert the following into logarithmic form :

1/1296  =  6-4

Solution :

log6(1/1296)  =  -4

Problem 7 :

Convert the following into logarithmic form :

(13)-1  =  1/13

Solution :

-1  =  log13(1/13)

Problem 8 :

Convert the following into logarithmic form :

8-2/3  =  1/4

Solution :

-2/3  =  log8(1/4)

Problem 9 :

Convert the following into logarithmic form :

10-1  =  0.1

Solution :

-1  =  log10(0.1)

Problem 10 :

Solve for x :

log1/5x  =  3

Solution :

log1/5x  =  3

Convert to exponential form.

x  =  (1/5)3

x  =  13/53

x  =  1/125

Problem 11 :

Solve for x :

logx125√5  =  7

Solution :

logx125√5  =  7

Convert to exponential form.

125√5  =  x7

5 ⋅ 5 ⋅ 5 ⋅ √5  =  x7

Each 5 can be expressed as (⋅ 5).

Then,

√5 ⋅ √5 ⋅ √5 ⋅ √5 ⋅ √5 ⋅ √5 ⋅ √5  =  x7

√57  =  x7

Because the exponents are equal, bases can be equated.

x  =  √5

Problem 12 :

Solve for x :

logx0.001  =  -3

Solution :

logx0.001  =  -3

Convert to exponential form.

0.001  =  x-3

1/1000  =  1/x3

Take reciprocal on both sides.

1000  =  x3

103  =  x3

Because the exponents are equal, bases can be equated.

10  =  x

Problem 13 :

Solve for x :

log5(5log3x)  =  2

Solution :

log5(5log3x)  =  2

Convert to exponential form.

5log3x  =  52

5log3x  =  25

Divide each side by 5.

log3x  =  5

Convert to exponential form.

x  =  35

x  =  243

Problem 14 :

Solve for x :

x + 2log279  =  0

Solution :

x + 2log279  =  0

x  =  -2log279

x  =  log279-2

Convert to exponential form.

27x  =  9-2

(33)x  =  (32)-2

33x  =   3-4

Because the bases are equal, exponents can be equated.

3x  =  -4

x  =  -4/3

Problem 15 :

Solve for x :

log3x + log9x + log81x  =  7/4

Solution :

log3x + log9x + log81x  =  7/4

(1 / logx3)  +  (1 / logx9)  +  (1 / logx81)  =  7/4

(1 / logx3)  +  (1 / logx9)  +  (1 / logx81)  =  7/4

(1 / logx3)  +  (1 / logx32)  +  (1 / logx34)  =  7/4

(1 / logx3)  +  (1 / 2logx3)  +  (1 / 4logx3)  =  7/4

(4 / 4logx3)  +  (2 / 4logx3)  +  (1 / 4logx3)  =  7/4

(4 + 2 + 1) / 4logx3  =  7/4

7 / 4logx3  =  7/4

Multiply each side by 4/7.

1 / logx3  =  1

log3x  =  1

Convert to exponential form.

x  =  31

x  =  3 After having gone through the stuff given above, we hope that the students would have understood how to do conversions between logarithmic and exponential forms.

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