5.6E: Logarithmic Properties (Exercises)

26. Rewrite \(\ln (7 r \cdot 11 s t)\) in expanded form.

27. Rewrite \(\log _{8}(x)+\log _{8}(5)+\log _{8}(y)+\log _{8}(13)\) in compact form.

28. Rewrite \(\log _{m}\left(\frac{67}{83}\right)\) in expanded form.

29. Rewrite \(\ln (z)-\ln (x)-\ln (y)\) in compact form.

30. Rewrite \(\ln \left(\frac{1}{x^{5}}\right)\) as a product.

31. Rewrite \(-\log _{y}\left(\frac{1}{12}\right)\) as a single logarithm.

32. Use properties of logarithms to expand \(\log \left(\frac{r^{2} s^{11}}{t^{14}}\right)\).

33. Use properties of logarithms to expand \(\ln \left(2 b \sqrt{\frac{b+1}{b-1}}\right)\).

34. Condense the expression \(5 \ln (b)+\ln (c)+\frac{\ln (4-a)}{2}\) to a single logarithm.

35. Condense the expression \(3 \log _{7} v+6 \log _{7} w-\frac{\log _{7} u}{3}\) to a single logarithm.

36. Rewrite \(\log _{3}(12.75)\) to base \(e\).

37. Rewrite \(5^{12 x-17}=125\) as a logarithm. Then apply the change of base formula to solve for \(x\) using the common log. Round to the nearest thousandth.