#2loga_x + loga_(ax) + 3loga_(a^2x) = 0#, Find #x# ?
1 Answer
Explanation:
The notation you have appears to be wrong, so I will assume that the first
Now, here are a few properties of logs that we need to look at:
1)
2)
3)
4)
To our equation then:
Applying Property 3 to the second and third terms we get:
distribute that 3:
Now use property 2 on that 4th term:
Now property 1 of the 2nd and 4th terms:
Adding all the
Now we use property 4 to change the base to 10 (a log without a base is in base 10):
Looking at those fractions, we can equate the top parts and the bottom parts, and since we aren't interested in
The last thing we need to remember is the definition of a log which is:
So now we have a known base for the log (10) a known quantity that the log is equal to (-7) so we just plug that in and get: