Indices, Surds & Logarithms

 

 

Contents

 

Indices

 

Laws of Indices

 

Surds

 

Laws of Surds

 

Exponential Equations

 

Logarithms

 

Laws of Logarithms

1  2 

Logarithmic Equations

 

Quiz

 

Algebra Main Page

Laws of Logarithms
 
 
Here are some examples on using the laws of logarithms.
Evaluate  log416 + log42 -log48 .
 
Solution:
 
        log416 + log42 -log48
            = log432 - log48                product law of logarithms
            = log44                            quotient law of logarithms
            = 1
 
 
Simplify logax + 3 loga (x + 1) - 2 logax .
 
Solution:
 
        logax + 3 loga (x + 1) - 2 logax
            = logax + loga (x + 1)3 - logax2        power law of logarithms
            = loga x (x + 1)3 - logax2                product law of logarithms
            =                            quotient law of logarithms
            =
 
 
Given that log52 = a and log53 = b, express the following in terms of a and b:
             (i)     log56
             (ii)    log50.75
             (iii)   log524
 
Solution:
 
            (i)     log56 = log52 + log53
                            = a + b
 
            (ii)    log50.75 = log53 - log54
                                = log53 - 2 log52
                                = b - 2a
 
            (iii)   log524 = log53 + log58
                             = log53 + 3 log52
                             = 3a + b