Simplify log₁₀(3/√(1+x)) using logarithm rules

[0range]

Homework Statement

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.

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

Homework Equations

The Attempt at a Solution

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

Thanks in advance!

 

[PeterO]

Homework Statement

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.

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

Homework Equations

The Attempt at a Solution

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.