Question

Give the answer for Log 45 base 2025=? And explain!

Answer 1

Answer:

$2025 = 81 \times 25 = {3}^{4} \times ( { \sqrt{5} })^{4} \\ 45 = 9 \times 5 = {3}^{2} \times ({ \sqrt{5} })^{2} \\ log_{45}(2025) = log_{ ({3 \sqrt{5} })^{2} }( {3 \sqrt{5} }^{4} ) \\ = \frac{4}{2} log_{3 \sqrt{5} }(3 \sqrt{5} ) = 2 \times 1 = 2$