1. ## Logarithmic Expression

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

2. ## Re: Logarithmic Expression

just use the power and product rules of logs

$\log_{10}(x^a)=a \log_{10}(x)$

$\log_{10}(a b) = \log_{10}(a)+\log_{10}(b)$

remember

$\sqrt{x}=x^\frac{1}{2}$

$\sqrt[3]{x}=x^\frac{1}{3}$

3. ## Re: Logarithmic Expression

Originally Posted by nycmath
Write the quantity using sums and differences of simpler logarithmic expressions. Express your answer so that logarithms of products, quotient and powers do not appear.
@nycmath, This may be the last reply I shall ever give you.
Frankly I am fed-up with your posting a raw question, but with your showing no effort whatsoever.

$\log \left[ {\sqrt[3]{{x\sqrt {1 + {y^2}} }}} \right] = \frac{1}{3}\left[ {\log (x) + \frac{1}{2}\log \left( {1 + {y^2}} \right)} \right]$

4. ## Re: Logarithmic Expression

I will show my part from now on. Perhaps you will be able to see where I went wrong.