Lesson 12- Laws of Logarithms

Laws of logs:

loga(xy)= loga^x + loga^y
loga(x/y)= loga^x - loga^y
*note: when logs multiply they will add together, when logs divide they will subtract eachother

logaX^n= nlogaX
loga^n (square root) x = logax 1/n
logaB= logb/loga

Express 5 as a power of 2:


2^x= 5             
xlog2= log5           log both sides!
x (log2/log2)= (log5/log2)        isolate x (divide logs)
x= 2.32

Express as a single logarithm:

log8 - log5
= log 8/5          (subtraction=division)

logB + logD - 5logE - logA^2 + 1/2 logA
log= BxDxA1/2
         E^5xA^2
= log BD
      E^5 xA3/2

Write in terms of log x and log y:

log100x^2y
log100 + logx^2 + logy
2 + 2logx +logy