Consider the following statements: Statement 1: If $ y = \log_{10}x + \log_e x $, then $ \frac{dy}{dx} = \frac{\log_{10} e}{x} + \frac{1}{x} $ Statement 2: $ \frac{d}{dx}(\log_{10}x) = \frac{1}{x \log 10} $ and $ \frac{d}{dx}(\log_e x) = \frac{1}{x \log e} $

Question

Consider the following statements:
Statement 1: If $ y = \log_{10}x + \log_e x $, then $ \frac{dy}{dx} = \frac{\log_{10} e}{x} + \frac{1}{x} $
Statement 2: $ \frac{d}{dx}(\log_{10}x) = \frac{1}{x \log 10} $ and $ \frac{d}{dx}(\log_e x) = \frac{1}{x \log e} $

Statement 1 is true; statement 2 is false

Statement 1 is false; statement 2 is true

Both statements 1 and 2 are true

Both statements 1 and 2 are false

Solution

Please login to view the detailed solution steps...

Go to DASH