Agenda• Don't forget about resources on
mrwaddell.net• Assignment from last class period• Sect 7.5: Properties of logarithms
Vocabulary
Exponentials
Logarithm
log x
ln x
Any equation of the form x=(b)y
The opposite of an exponential equation
y= logb x
No base? It is automatically base 10!
“ln” is a shortcut way to writeloge said “log base e”
Property of Logs and Exponents
One-to-One Property of Exponential Functions and logs
If bx = by, then x = y.
If logb x = logb y, then x = y.
Practice ProblemsWrite each expression as a single logarithm. Then simplify if possible.
log25 + log27
log2 (5∙7)
problem
product property
log2 (35) finished
Practice ProblemsWrite each expression as a single logarithm. Then simplify if possible.
Log536x3
Log536 + Log5x2
problem
product property
Log536 + 2Log5x Power property
Practice ProblemsWrite each expression as a single logarithm. Then simplify if possible.
problem
quotient property
product property
𝑙𝑛 10𝑥5
𝑦 4
𝑙𝑛10 𝑥5− 𝑦4
𝑙𝑛10+ 𝑙𝑛𝑥5−𝑦 4
𝑙𝑛10+5 𝑙𝑛𝑥− 𝑦4 power property
Practice ProblemsWrite each expression as a single logarithm. Then simplify if possible.
log48 + log42
log4(16)
problem
product property
log4 (4∙4) Hmm, what exponent for 4x =16
2 is the answer!
Practice ProblemsWrite each expression as a single logarithm. Then simplify if possible.
log335 - log5125
5log33 – log5(5∙5∙5)
problem
power prop & factoring
Inverse prop
2 is the answer!
5 – log5(5∙5∙5)
5 – 3 How many 5’s are there again?