Problem 2: Write this expression as a sum or difference: (√¹) In ln( \sqrt{ (x - 1)/(x) } ) ​

Question

Problem 2: Write this expression as a sum or difference: (√¹) In


`ln( \sqrt{ (x - 1)/(x) } )`
​

Answer 1

Answer: 1/2 ln (x-1) - 1/2 ln x

Explanation:

Answer 2

`~~~\ln \left( \sqrt{\frac{x-1}x \right )\\\\\\=\ln\left((√(x-1))/(\sqrt x) \right)\\\\\\=\ln\left(√(x-1) \right) - \ln \left( \sqrt x \right)~~~~~~~~~~~~~~~~~~~~;\left[\log_b\left( \frac mn \right) = \log_b m - \log_b n \right]\\\\\\=\ln\left[\left(x -1\right)^(\tfrac 12) \right] - \ln\left(x^(\tfrac 12) \right) \right)\\\\\\=\frac 12 \ln(x-1) - \frac 12 \ln x~~~~~~~~~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]`