How do you solve #log x + log(5 – x) = 0#?
The key realization here is that we can use the logarithm property
which can be simplified to
We essentially now have
Notice, what we have in blue is also equal to
Both sides of the equation have
What's left is
Turning this into a quadratic, we get
We can now apply the Quadratic Formula,
Plugging in, we get
Which simplifies to
Thus, our roots are equal to
Hope this helps!