What is the true solution to the equation below? 2log3(6x)-log3(4x)=2log3(x+2)

  x = 1 and x = 4

Step-by-step explanation:

A graph of the given equation, after rewriting to make the solutions be zeros of the function, shows the solutions to be x = 1 and x = 4.

You can take the antilog and solve the quadratic:

  log3((6x)^2/(4x)) = log3((x+2)^2) . . . . consolidate the logs

  9x = (x +2)^2 . . . . simplify and take the antilog

  0 = x^2 -5x +4 . . . subtract 9x

  0 = (x -4)(x -1) . . . . factor

Solutions are x = 1 and x = 4. (These values make the factors zero.)

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.