log (x+8) - log x = 3 log 2 ( SOLVE exactly for X)

[wilc0919]

log (x+8) - log x = 3 log 2

Not sure where to START here....I thought I understood the lecture but I am STUMPED now....can someone help me out?

 

[stapel]

log (x+8) - log x = 3 log 2

Not sure where to START here.

Apply a log rule:

. . . . .log(x + 8) - log(x) = log[(x + 8) / x]

Also:

. . . . .3 log(2) = log(2³) = log(8)

Set them back equal to each other, and equate the arguments. Solve the resulting rational equation.

Eliz.

 

[wilc0919]

I end up with

log (x+8) / x is equal to log 2 ^3

then I get

log (x+8) / x = log 8

so I get log (x+8) / x = .9031

THEN WHAT? I am new to logs and don't really know what to do with the equation after that.

 

[stapel]

"Set them back equal to each other, and equate the arguments. Solve the resulting rational equation."

Eliz.

 

[wilc0919]

"Set them back equal to each other, and equate the arguments. Solve the resulting rational equation."


I have no idea what this means or where to start, I am stupid and very new to math....how do I solve?

log (x+8) / x = log 8

 

[stapel]

If log(this) equals log(that), and the logs have the same base, then doesn't "this" have to equal "that"?

Eliz.

 

[wilc0919]

so confused

I have no idea what to do or where to go after I get to

log(x+ 8) / x (I am so confused by the fraction...don't have any clue what to do here.....


what is the next step in log (x+8) / x = .90308

 

[stapel]

I have no idea what to do....

Have they not covered logarithms or log equations in your class? That's rough. This topic can be confusing, and lessons would have been helpful.

Just as I said earlier, if log(this) = log(that), then "this" must equal "that". Since "this" and "that" are the "arguments" (most lessons on logs will teach you about this term), then, when I said "equate the arguments", that meant the same thing as when I said to get "this" and "that" equal to each other.

So, instead of evaluating the log on the right-hand side of the equation, try following the instructions: Set the insides of the left-hand side's log equal to the right-hand side's log. This will create a rational equation that you can solve.

Please let me know if you need links to online lessons, so that you can get up to speed on this topic. It's not too bad, but you do need the foundational concepts.

Thank you.

Eliz.