How can I calculate the right ratio

Question

I m currently preparing for sat subject mat 2 exam and whenever this type of question comes , answer that my calculator gives and the answer key says doesn't match. Does anybody can help , maybe suggestions for a different approach ?

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I do the same thing in my calculator but get an answer 1.389975. I m using casio fx cg50 enter image description here

Answer 1

Take logs on both sides

$$\ln(8.1^a)=\ln(3.6^b)$$ Apply properties $$a\ln(8.1)=b\ln(3.6)$$ $$\therefore \frac{a}{b}=\frac{\ln(3.6)}{\ln(8.1)}≈ 0.61$$

Thus the answer is B