I've got the equation:
$$\log_{10}(x^2 – 16) – 3\log_{10}(x + 4) + 2\log_{10} x$$
I'm looking to express this as a single logarithm. I came up with
$$\log_{10}(x^2 – 16) – \log_{10}(x + 4)^3 + \log_{10} x^2$$
then
$$\log_{10} \left(\frac{x^2(x^2 – 16)}{(x + 4)^3}\right) $$
Please forgive me if I got the number of parentheses wrong.
This looks like the results of most of the examples, would you think further simplification is required?
Best Answer
Your reasoning is absolutely right! However, there is one final simplification you can make: to the fraction $$\frac{x^2(x^2 - 16)}{(x + 4)^3}$$ itself. Hint: Can you factor $x^2-16$?