AP EAMCET · Maths · Basic of Mathematics
If the two curves \(\mathrm{y}=a^x\) and \(y=b^x\) intersect at angle \(\alpha\), then \(\tan \alpha=\)
- A \(\frac{\log a-\log b}{1+\log a \log b}\)
- B \(\frac{\log a+\log b}{1-\log a \log b}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{\log a-\log b}{1+\log a \log b}\)
Step-by-step Solution
Detailed explanation
Given \(y=a^x, y=b^x\) \(\mathrm{a}^{\mathrm{x}}=\mathrm{b}^{\mathrm{x}} \Rightarrow \mathrm{x}=\mathrm{o}\) \(\therefore\) curves \(\mathrm{y}=\mathrm{a}^{\mathrm{x}}\) and \(\mathrm{y}=\mathrm{b}^{\mathrm{x}}\) intersects at \(\mathrm{x}=\mathrm{O}, \mathrm{y}=1\) Let…
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