I've just been accepted on to a PHD program at Melbourne, studying chemical engineering.
I'm working my way through some standard pure and further mathematics books just to get the concepts into my head before I start. Some of this I won't need, but maths is invaluable in the sciences anyway.
I've been going through some logs and exponentials questions. I've found that I'm doing really well, i've just come across one set of questions and between flicking back and forth from the laws of logs and exponentials and the questions themselves, I'm getting a bit frustrated.
The textbook is asking me to find $a$ if:
1) $\log_a 8 = \frac 3 2$
2) $\log_a 25 - \log_a 0.25 = 2$
3) $\log_2 a - \log_8 a = 4$
In terms of doing the same to both sides, where is the most logical place to start? Clearly for the first it is to multiply both sides by $2$ so I have $2 \log_a 8 = 3$.