# Another logarithm simplification exercise.

1. Aug 7, 2011

### 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

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

2. Aug 7, 2011

### PeterO

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

3. Aug 7, 2011

### 0range

No, the original equation is as appears.

4. Aug 7, 2011

### eumyang

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

5. Aug 7, 2011

### 0range

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

Thanks again.