Evaluate Log Expression Using Change-of-Base Formula
Let m  log b  x 
Rewrite m  log b  x  in exponential form:
bm = x
log10  b m  = log10  x 
Take log10 of each side
m  log10  b  = log10  x 
Apply Power Rule
m  log10  b 
log10  b 
m=
=
log10  x 
log10  b 
log10  x 
log10  b 
log b  x  =
log10  x 
log10  b 
log 7  5  
log10  5 
log10  7 
log 7  5   0.8270874753
log17  225  
log10  225 
log10 17 
log17  225   1.911645804424
log 27   
log10  
log10  27 
log 27    0.3473260153
Change-of-Base Formula
 5  log10  5 / 9 
log1/3   
 9  log10 1/ 3
5
log1/3    0.5350264793
9
log  55555  
log10  55555 
log10  
log  55555   9.5438486713
Practice Problems
1) Evaluate log 5 7
2) Evaluate log 6 12
3) Evaluate log 7 147
4) Evaluate log 8 125
5) Evaluate log  560 
6) Evaluate log e  515 
Note: e  2.718281828
7) Evaluate log 1520 
8) Evaluate log e  224 
9) Evaluate log 7 147
10) Evaluate log18.2 125.35
11) Evaluate log 7.5 1.547
12) Evaluate log 8.3 12.2565
Note: e  2.718281828