Using the Properties of Logarithms with Numerical Values

Question

Given the approximations log 2=0.3010 and log 3 = 0.4771, find each logarithm without using a calculator.

 

log 20/27

 

 

I'm having a really hard time with this one. I've read the instructions in the book over and over and its just not clicking for me.

Answer 1

Find log 20/27 given  log 2=0.3010 and log 3 = 0.4771

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Robert has the correct answer.  The rules application are what you
need to understand.
 
1)  For the log of quotients:  log a/b = log a - log b, thus
     log 20/27 = log 20 - log 27
  
2)  log of products is the sum of the two logs... log ab = log a + log b, thus

     log 20 - log 27 = log(2*10) - log27 

     = log 2 + log 10 - log 27

 
3) Log is considered to be base 10 unless a different base is specified.
    log 10 = 1og₁₀10 = 1   so

    log 2 + log 10 - log 27 = log 2 + 1 - log 27

 
4) For logarithms with exponents:  log aⁿ = n log a

    log 27 = log 3³ = 3 log 3    so

    log 2 + 1 - log 27 = log 2 + 1 - 3 log 3

 

You are given log 2 = 0.3010  and log 3 = 0.4771

Substitute those into this expression

 

.3010 + 1 - 3(.4771) = -0.1303  
 

Answer 2

log(20/27)=log(20)-log(27)

        

               =Log(2)+log(10)-3*log(3)

 

              =0.3010+1-3*0.4771= -0.13030