log questions times 3

[Guest]

I need help with these questions:

1) Solve: log₅(2x+2) - log₅(x-1) = log₅(x+1)

After cancelling the log₅ I get stuck: [(2x+2)/(x-1)]-(x+1)=0

2) If log₂(log₃(a)) = 2, determine the value of a.

3) If logsubscript 2 subscript n (1944) = logsubscriptn (486 2square rooted), determine the value of n^6.

The last two questions just confuse me.

-thanks for the help

 

[stapel]

1) What do you mean by "cancelling the log₅"? Do you mean that you used a log rule to combine the logs on the left-hand side and that, once you'd had "log₅(something) = log₅(something else)", you'd equated the arguments of the logs?

If so, you'd have had:

. . . . .\(\displaystyle \large{\frac{2x\,+\,2}{x\,-\,1}\,= \,x\,+\,1}\)

Has your algebra class not yet covered how to solve proportions or rational equations? The usual procedure for such an exercise would be to "cross-multiply" and solve the resulting quadratic equation. Does any of that sound familiar?

2) Hints: If log₂(x) = 2, what is x?

If log₃(a) = x, what is a?

3) I'm sorry, but I can't figure out what you mean on this one. Is the first log "base 2n", or "base 2_n", or something else?

Thank you.

Eliz.