Log Basics
ln
Logs can only be condensed if they have.....
The same log base
Expand: log2xyz
log2 + logx + logy + logz
Expand: log4/x
log4 - logx
Expand: logx^5
5logx
What is the common log?
base 10
How many times will log be written?
log9x^3/2y
3 times
Condense: log8 + loga + logb
log8ab
Condense: log10-x - logy
log10-x/y
Condense: xlog17
log17^x
What formula says log _3 (5) (log base 3 of 5) is equal to log 5 / log 3?
Change of base formula
Steps in Order:
log7 + 2logx - log3+y
1) Power Property: logx^2
2) Product Property:log7x^2 - log3+y
3) Quotient Property: log7x^2/y
Can there be negative numbers?
No
The number in the denominator means...
the number that will be subtracted
Does the exponent get its own log?
No
Solve for x.
log (1) = x
0
Steps in Order:
log9x^y/z
1) Product Property: log9 + logx^y
2) Quotient Property: log9 + logx^y - logz
3) Power Property: log9 + xlogy - logz
When to use the Product Property?
Where there is multiplication/addition present.
When to use the Quotient Property?
Where division/subtraction is present.
When to use the Power Property?
With a coefficient of the log or exponent of the term inside the log.
What is the domain of Logarithms?
(Hint:Think about what you cannot take the log of)
D : (0,infinity)
x > 0
log(z^5 * √(x))/(y)
5log z + 1/2logx - log y
Which step should the Product Property be used when expanding?
First
Which step should the Quotient Property be used when expanding?
Second
simplify :
log (10^7x)
7x