Question

solve the following equation

Log1/3(x2+x)-log1/3(x2-x)=2

the 1/3 should be lowered and the (x^2-x) should be higher. Can someone tell me what tools to use to make them like this when posting?

x= ?

Answer 1

so the base of the log is 1/3

in general exponentiation is show with the ^ symbol
e.g. x^2 means "x squared"

subscripts are are more difficult but are usually described like you did, as long as they are well defined tutors will be able to figure it out

log_1/3 (x^2 + x) - log_1/3(x^2 - x) = 2

log_1/3 [ (x^2+x)/(x^2-x)] = 2

(x^2+x)/(x^2-x) = (1/3)^2 = 1/9
cross-multiply
9x^2 + 9x = x^2 - x
8x^2 + 10x = 0
x(8x+10) = 0
x = 0 or -5/4 or -1.25

but x = 0 would make both log_1/3 expressions undefined

check:
if x= -1.25
we have
log_1/3.3125 - log_1/32.8125
which is defined


so x = -1.25 or -5/4