Write in terms of x, y, and z. *

We want to write the expression such that the variables are as isolated as possible.
Solve	Step	Property
	Start with division  division turns into subtraction
=  log 3 + log x - (log y + log z)	Take care of multiplication next  multiplication turns into addition	log b MN = log b M + log b N
=  log 3 + log x - log y - log z	Distribute the minus sign	Recall: log  x = log 10 x
	All variables are isolated
* Assume all values for x, y, and z are defined for each expression. Example log (-2) is undefined.

  

Write in terms of the logarithms  of x, y, and z.

	[Solution]

Write in terms of the logarithms  of x, y, and z.

 

We want to write the expression such that the variables are as isolated as possible.
Solve		Step	Property
		Start with division  division turns into subtraction
Recall:		Convert radicals into exponents
		Replace radicals
		Exponents turn into multiplication	log b M p  = p log b M
		Take care of multiplication next  multiplication turns into addition	log b MN = log b M + log b N
		Do  log b x2 = 2 log b x next	log b M p  = p log b M
		Distribute 1/3 through ( )
		All variables are isolated
* Assume all values for x, y, and z are defined for each expression. Example log (-2) is undefined.

 

Write in terms of the logarithms  of x, y, and z.

	[Solution]

Evaluate the following to 3 decimals places:    log 2 5

Solve	Step	Property
	Change of Base formula
HINT: use these key strokes	log 5 ÷ log 2 [enter or =]

Evaluate the following to 3 decimals places:    log 5 2

	[Solution]

Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada