true-or-false-for-positive-real-numbers-m-and-gt0-m-and-gt-0-and-n-and-gt0-n-and

Question

Given the integral definition ln⁡c=∫1c1t dt \ln c = \$$int_1^c$$ \frac{1}{t} \, dt , which of the following expressions is equivalent to ln⁡(mn) \ln\left(\frac{m}{n}\right) ?

Accepted Answer

∫nm1tdt\int_{n}^{m}\frac{1}{t}dt

Answer

∫1m1tdt+∫1n1tdt\$$int_1$$^{m}\frac{1}{t}dt+\$$int_1$$^{n}\frac{1}{t}dt

Answer

∫mn1tdt\int_{m}^{n}\frac{1}{t}dt

Answer

∫1mn1tdt\$$int_1$$^{mn}\frac{1}{t}dt

Given the integral definition lnc=∫1c1tdt \(\ln\) c = \(\int\)_1^c \(\frac{1}{t}\) \, dt , which of the following expressions is equivalent to ln(mn) \(\ln\[\left\)(\(\frac{m}{n}\]\right\)) ?

Given the integral definition $\ln c = \int_{1}^{c} \frac{1}{t} d t$ , which of the following expressions is equivalent to $\ln (\frac{m}{n})$ ?