Where appropriate, include the approximation to the nearest ten-thousandth.

Question

31.) log(x-4)+ log(x+4)= log4
I have the answer as 4

Is this answer right?

Answer 1

log a + log b is same as log ab

so log(x^2-4)=log4
taking antilogs
x^2-4=4 solve for 4
check my thinking.

Answer 2

Okay x^2-4 = 4

x^2= 8

sqrt(x^2)= sqrt 8

x= 2.83 is this right?

Answer 3

log k has a nasty habit of becoming undefined if k is not positive.

you answer of x = 2.832 is correct according to the steps taken, but...

when we sub into log (x-4) we get log (-1.168 which is undefined,

so there is no solution in the set of real numbers for your equation

Answer 4

Going back and looking over the previous solutions, I noticed that the original non-log equation should have said:

x^2-16 = 4
so x^2 = 20
x = √20 = 4.472136

which works upon substituting.