Help with a logarithim approximation other than base 10.

ochocki

New member
Joined
Feb 7, 2005
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46
I am stumped by this logarithim approximation:

. . .log<sub>1/2</sub>(5)

I know that I need to use the change-of-base formula:

. . .log<sub>b</sub>(a) = log<sub>c</sub>(a) / log<sub>c</sub>(b)

So I plug in numbers for the variables, rounding decimals at the 4th decimal place:

. . .log<sub>1/2</sub>(5) = log(5) / log(1/2) = 0.6990 / -0.3010

When I divide them, I get -2.3223 as my approximation, but the book says the answer is -2.3219

Can anyone tell where I am going wrong so I can correct my mistakes?
Thank you!
 
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