Another logarithm simplification exercise.

[0range]

1. The problem statement, all variables and given/known data

Write the quantity using sums and differences of simpler logarithmic expressions. Express the answer so that logarithms of products, quotients, and powers do not appear.

log_{10}\frac{3}{\sqrt{1+x}}


2. Relevant equations



3. The attempt at a solution

http://i52.tinypic.com/2czc1sh.jpg

The book's answer, however, is 3log_{10}x-\frac{1}{2}log_{10}(1+x)

Thanks in advance!

[PeterO]

1. The problem statement, all variables and given/known data

Write the quantity using sums and differences of simpler logarithmic expressions. Express the answer so that logarithms of products, quotients, and powers do not appear.

log_{10}\frac{3}{\sqrt{1+x}}


2. Relevant equations



3. The attempt at a solution

http://i52.tinypic.com/2czc1sh.jpg

The book's answer, however, is 3log_{10}x-\frac{1}{2}log_{10}(1+x)

Thanks in advance!

Check the original question to make sue the numerator is just 3 and not an exponential

[0range]

Hi, thanks for the reply.

No, the original equation is as appears.

[eumyang]

Must be a typo in the book, then. Possibly whoever typed up the answer key thought that the problem was
log_{10}\frac{x^3}{\sqrt{1+x}}

[0range]

Oh, so I'm right? How anti-climatic...

Thanks again.