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6.5E: Logarithmic Properties (Exercises)

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    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.

    This page titled 6.5E: Logarithmic Properties (Exercises) was last modified on Thu, 26 Dec 2024 22:31:00 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.