Question

Please & thank you!
Use properties of logarithms to solve the equation.
log(base3) x + log(base3)(x + 2) = log(base3) 2 + log(base3) 12

Answer 1

as i can recall log(ab)=loga+logb
use this property

Answer 2

i dont understand how to solve it though

Answer 3

\[\large{log_3 x+log_3 (x+2)=log_3 2+log_3 {12}}\]

Answer 4

\[\large{log_3(x(x+2))=log_3(2*12)}\]

Answer 5

x(x+2) = 24

Answer 6

can you solve further?

Answer 7

would the answer just be be one?

Answer 8

just tell me what is x(x+2)

Answer 9

x^2 + 2x

Answer 10

\[\large{x^2+2x-24=0}\]
\[\large{x^2+6x-4x-24=0}\]
\[\large{x(x+6)-4(x+6)=0}\]
\[\large{(x-4)(x+6)=0}\]

Answer 11

hence we have x = 4 or x = -6

Answer 12

why is it -24 and not just 24

Answer 13

x^2+2x=24
right?

Answer 14

now subtract 24 both sides
x^2+2x-24=24-24
x^2+2x-24=0

Answer 15

oh okay! thank you!

Answer 16

no problem and best of luck

Answer 17

thanls

Answer 18

but remember only the positive answer is accepted

Answer 19

would it be wrong if i gave the negative answer as well?

Answer 20

yes