Condense
How many times do you write log/ln?
Once
How many times do you write log/ln?
Multiple times
Expand: log2xyz
log2 + logx + logy + logz
Expand: log4/x
log4 - logx
Expand: logx^5
5logx
Is this Condensed fully?
xlog2/y
No: Did not use Power Property
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
Purpose of condensing logs
To compress a logarithmic expression into one logarithm
Purpose of expanding logs
To divide the logarithmic expression into many individual parts.
Can there be negative numbers?
No
The number in the denominator means...
the number will be negative.
Does the exponent get its own log?
No
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
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?
Where an exponent/rationals are present.
½log(9x+3) - log24
log√(9x+3)/4
logx^4√(6y)/(2z)^3
4logx + ½log6y - 3log2z
Which step should the Product Property be used when expanding?
First
Which step should the Quotient Property be used when expanding?
Second
Which step should the Power Property be used when expanding?
Third