Logarithms

The logarithm of a number is the exponent to which another fixed value, the base, has to be raised to produce that number.

The logarithm of b to base a, if a>0 and a≠1, is:

Examples:

Properties:

 

 

 

 

 

Example: If log 5 ≈ 0.7, then calculate log 50, log₅10, log 2 and log 125

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Exercises:

1.- Calculate:

a) log 0.01=

b) log₃⁵√81²=

c) log₇(⁵√49/⁴√343)=

 

2.- If ln 5 ≈1.6, calculate:

a) ln 5e =

b) ln √(e/25)=

c) ln⁴√125=

 

 

 

Solutions: 1.- a) -2; b) 4/5; c) -7/20; 2.- a) 2.6; b) -1.1; c) 1.2