week 3 10 question

Question

Solve the following logarithmic equation:

log₇x + log₇(3x-2) = 0

Be sure to check all of your solutions in the original equation.

please show steps

Answer 1

log x + log (3x - 2) = 0

7 7

log (x) (3x - 2) = 0

7

log (3x^2 - 2x) = 0

7

since log b = x then a ^x = b

a

0

3x^2 - 2x = 7 = 1

3x^2 - 2z - 1 = 0

(3x + 1)(x - 1) = 0

x = -1/3 or 1

only works for x = 1