Order of Applying Log Properties

[Lime]

The problem:

= 3 [log_b X - log_b Y + log_b Z^2]

In the solution book, the next step is:

= 3 [log_b (X Z^2) - log_b Y]

I see what they did, but what that and not this:

= 3 [log_b X - log_b (Y Z^2)]

And both methods resulted in different final answers.

 

[stapel]

Assuming that the instructions were to combine the logs into a single log expression, the order of the operations doesn't matter, so long as you're applying the same operations.

The book, effectively, did "X - Y + Z = (X + Z) - Y". You tried to turn this into "X - (Y + Z)". But X - (Y + Z) = X - Y - Z, which is not what you started with.

Verdict: Be very careful with your signs!

Eliz.