Which of the following is true regarding the solutions to the logarithmic equation below?
2logg(x) = 2
10g6(x? ) = 2
x2 = 36
x=6,-6
x= 6 and x=-6 are true solutions
x=6 and x=-6 are extraneous solutions
x=6 is a true solution and x=-6 is an extraneous solution
x= 6 is an extraneous solution and x=-6 is a true solution

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)

i think the answer would be c