SOLUTION: Show that {{{x=2sqrt(254)}}} is the solution of {{{log10(x-4)+log10(x+4)=3}}} i found the answer to this question but i haven't been able to do it with others like it so if you

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Show that {{{x=2sqrt(254)}}} is the solution of {{{log10(x-4)+log10(x+4)=3}}} i found the answer to this question but i haven't been able to do it with others like it so if you       Log On


   

Question 997234: Show that x=2sqrt%28254%29 is the solution of log10%28x-4%29%2Blog10%28x%2B4%29=3
i found the answer to this question but i haven't been able to do it with others like it so if you could help with the working out that would be great!!
THanks!!
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
A guess that you mean to start with log%2810%2C%28x-4%29%29%2Blog%2810%2C%28x%2B4%29%29=3

log%2810%2C%28%28x-4%29%28x%2B4%29%29%29=3
log%2810%2C%28x%5E2-16%29%29=3
10%5E3=x%5E2-16
x%5E2=10%5E3%2B16
x%5E2=1000%2B16
x%5E2=1016
x%5E2=2%2A508=2%2A2%2A254=2%2A2%2A2%2A127, best stated as x%5E2=2%2A2%2A254 because the 127 is a prime number.
%28x%5E2%29%5E%281%2F2%29=%282%2A2%2A254%29%5E%281%2F2%29
x=2%2A254%5E%281%2F2%29 or x=2%2Asqrt%28254%29