Question 549397
    I'm completely done with my assignment, But i'm on my last question and it's a critical thinking question. It says, 2(log 2x - log y)-(log 3 + 2log 5). I got told the answer is: log 4x^2/75y^2 but i don't know how to work it out and explain my work. It's a difficult question and if you could help me that would be great. Thanks for your help. 
You need to apply "log rules":
2(log 2x - log y)-(log 3 + 2log 5)
distribute the 2 and remove parentheses:
2log 2x - 2log y-log 3 - 2log 5
multiplier of a log can be thought of as an exponent:
log(2x)^2 - logy^2 - log(3) - log 5^2
subtraction can be thought of as division:
log(4x^2) - logy^2 - log(3) - log 25
log(4x^2)/y^2 - log(3) - log 25
log(4x^2)/3y^2 - log 25
log(4x^2)/(75y^2)