Help with Logarithm questions.?

I'm going to use _ as a subscript indicator (in this case indicating the logarithmic bases) so as to make this more convenient.

I also use ^ as an exponentiation indicator.

Question 1:

[log_7 (32)] / [log_7 (8√2)]

= [log_7 (2^5)] / [log_7 (2^(3.5))]

= [5 log_7 (2)] / [3.5 log_7 (2)]

= 5 / 3.5

= 10/7

[This one was somewhat amusing in that the logarithmic base never matters. It only matters that it's the same base in both numerator and denominator, so we can cancel out the factors of log_7(2).

Question 2:

[log_a (18) + log_a (12) - log_a (125)] / [log_a (42) - log_a (35)]

= [log_a (18*12/125)] / [log_a (42/35)]

= [log_a (216/125)] / [log_a (6/5)]

= [log_a ((6/5)^3)] / [log_a (6/5)]

= [3 log_a (6/5)] / [log_a (6/5)]

= 3

and again, we get to cancel out log_a (6/5) and obtain a simple answer.