Solve the logarithmic equation. Please show all of your work.

Question

Loga(x+4) + loga(x-4) = 4

Answer 1

lgt(a)+lgt(b)=lgt(a*b)

lgt(x+4)+lgt(x-4)=4

lgt[(x+4)*(x-4)]=4

lgt is the logarithm with base 10.

Antilogarithm of this expresion is

(x+4)*(x-4)=10^4

(x+4)*(x-4)=10.000

x^2+4x-4x-4*4=10.000

x^2-16=10.000

x^2=10.000+16

x^2=10.016

x=sqroot(10.016)

x=100.0799680256