Question 825624
log(x+16) = log(x) + log(16)
First we use a property of logarithms, {{{log(a, (p)) + log(a, (q)) = log(a, (p*q))}}}, to combine the two logs on the right into one:
log(x+16) = log(x*16)
or
log(x+16) = log(16x)<br>
This equation says that two base 10 logs are equal. The only way this can be true is if the arguments are equal, too. So:
x+16 = 16x
Now we can solve for x. Subtracting x from each side:
16 = 15x
Dividing by 15:
{{{16/15 = x}}}<br>
One way to see if this result is in the domain is to try this solution in the original equation and see if all the arguments are valid (i.e. positive):
{{{log(((16/15) + 16)) = log((16/15)) + log(16)}}}
We should already be able to see that all three arguments will be positive. So 16/15 is in the domain and is a valid solution to the problem.