Blog Post 4 Logarithmic Functions

Hello Class! My name is Tyler Hooper and today we will be learning about Logarithmic Functions.

Logarithmic Functions are the opposite of exponential functions. Contains base "b".

• For x > 0,  b>0, b cannot equal 1
• y=logbx if and only if b^y=x
• in both equations y= output, b= base, x=argument
• f(x)=logbx is read "log base b of x"

Common Logarithmic Functions

• for x > 0, y=log10X if and only if  10^y=x
• When no base is given the base is understood to be 10 and this is known as a common log.
• Here are some examples
• y=log2X => x=2^y if x=32, y=5 because 2 raised to the fifth power equals 32
• y=logX => x=10^y if x=100, y=2 because 10 squared is 100

Natural Logarithmic Functions

• Contain Base "e"
• When written with out base e it is assumed that it is there--> lne=ln
• y=logeX => y=lneX if and only if e^y=x
• Example: ln(x+1)=2 => e^2=x=1

Properties of Logs

• Zero Property
• Common Logs: logb1=0 => b^0=1
• Natural Logs: ln1=0 => e^0=1
• Identity Property
• Common Logs: logbb=1
• Natural Logs: lne=1
• Inverse Property
• Common Logs:logbb^x=x
• Natural Logs:lne^x=x
• 1-1 Property
• Common Log: logbx=logby => x=y
• Natural Logs: lnx= lny => x=y
• Product Property
• log(uv)=logu + logv
• Quotient Property
• log(u/v)= logu - logv
• Power Property
• logu^n=nlogu