1

Logarithms

Definition

If y = ax then x = logay

For log10x use the log button.

For logex use the ln button.

2

Logarithms

Examples

Log105.3 =

0.724275869 ≈

0.7

Log1053 =

1.724275869 ≈

1.7

Log10530 =

2.724275869 ≈

2.7

Loge5.3 =

1.667706821 ≈

1.7

Loge53 = 3.970291914 ≈

4.0

Loge530 =

6.272877007 ≈

6.3

3

Logarithms

Example 1

Log327 = x

If y = ax then x = logay

27 =

3x

33 = 3xx = 3

y = 27 a = 3 x = x

4

Logarithms

Example 2

Log381 = x

If y = ax then x = logay

81 =

3x

34 = 3xx = 4

y = 81 a = 3 x = x

5

Logarithms

Example 3

Log264 = x

If y = ax then x = logay

64 =

2x

26 = 2xx = 6

y = 64 a = 2 x = x

6

Logarithms

Example 4

Log21/4 = x

If y = ax then x = logay

1/4 = 2x

2-2 = 2x

x = -2

y = 1/4 a = 2 x = x