C2 logs help...

john23

2

How do you solve:

2log3 x - log3 (x-2) = 2 ,when, x is more than 2

Reply 1

Chewwy

17

log3 (x^2) - log3 (x-2) = 2
log3 (x^2 / (x-2)) = 2
x^2 / (x-2) = 3^2 = 27
x^2 = 27x - 52

oh look, a quadratic.

Reply 2

Trangulor

6

a{log_b{c}}=log_b{c^a}

log_b{a}+log_b{c}=log_b{ac}

Reply 3

Mos Def

17

hey i get something else :s-smilie:

...but i think im wrong as both my solutions are above 2.

2log3x - log3 x-2 =2

log3 x²/ x - 2 = 2

put everything as the power 3

x²/x -2 = 9

x² = 9 (x - 2)

x² = 9x - 18

x² - 9x + 18 = (x - 6)(x-3)

i.e. x = 6 or 3 ...so as i get 2 answers above +2 i am not sure about this.

choochie howd you get 27?

Reply 4

hatty341

8

T_Bag

hey i get something else :s-smilie:

...but i think im wrong as both my solutions are above 2.

2log3x - log3 x-2 =2

log3 x²/ x - 2 = 2

put everything as the power 3

x²/x -2 = 9

x² = 9 (x - 2)

x² = 9x - 18

x² - 9x + 18 = (x - 6)(x-3)

i.e. x = 6 or 3 ...so as i get 2 answers above +2 i am not sure about this.

choochie howd you get 27?

i got 6 and 3 as well using the same method...