exam Maths Puzzle Numerical Ability

I need help with this expression.
logA/logB = A/B = 2/3. 2/3 is the correct answer, but the student who did this problem canceled the logs. What are A and B?

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exam Other Question

Can someone please help me with this division problem? I am totally lost.

(3-x+8x^3-10x^2)/(1+2x)
Please help to add :

5/x + 6/x^2 - 4 - 3x / 2 - x