Question 250999
log(x^2 - 100) = 1 + log(x + 10)
:
We can factor the expression on the left (it's the "difference of squares")
log ((x-10)(x+10)) = 1 + log (x + 10)
:
Subtract log(x+10) from both sides
log ((x-10)(x+10)) - log (x + 10) = 1
:
Can be written as, (subtraction of logs means divide)
{{{log((((x-10)(x+10))/(x+10)))}}} = 1
:
Cancel (x+10) and you have:
log(x-10) = 1
:
exponent equiv of logs
10^1 = x - 10
10 = x - 10
10 + 10 = x
x = 20
:
Check this solution on your calc, enter
log(20^2 - 100) - log(20 + 10) results = 1