Logarithms Plus Order of Operations Confusion

[MurraySchwartz]

I am working out a formula in statistics which looks like this:

Z = 1/2LOG_e (1+r/1-r)

Where r = 0.87

Z = 1/2LOG_e (1.87/-0.87)

The problem is I have a negative number as the denominator and I don't know how to deal with it.

I thought it could be re-written as 1/2 * (LOG_e 1.87 - LOG_e 0.87) leading to:

1/2 * (.63 - (-.14)) = 1/2* .76 = .382

Unfortunately the book gives an answer of 1.33.....I cannot figure out why. I am hoping someone can help me remove my blinders.
Thanks

 

[Quaid]

I am working out a formula in statistics which looks like this:

Z = 1/2LOG_e[(1+r)/(1-r)]

Where r = 0.87

Z = 1/2LOG_e (1.87/-0.87)

The problem is I have a negative number as the denominator and I don't know how to deal with it.

I thought it could be re-written as 1/2 * (LOG_e 1.87 - LOG_e 0.87) leading to:

1/2 * (.63 - (-.14)) = 1/2* .76 = .382

Unfortunately the book gives an answer of 1.33.....I cannot figure out why. I am hoping someone can help me remove my blinders.
Thanks

Hi Murray:

An arithmetic error is highlighted in boldface red above.

Cheers

 

[MurraySchwartz]

An arithmetic error is highlighted in boldface red above.

Thanks. But how can there be a log with a negative in the denominator that works out to be a positive answer as the book says...I don't understand that part of the process.....

 

[MurraySchwartz]

1 - .87 = .13 ; have a closer "look"!

Thanks....Amazing I could not see that simple thing....I appreciate your help.....