Question 4.4.5.8: Using the Change-of-Base formula Approximate: (a) log5 89 (b......
Using the Change-of-Base formula
Approximate:
(a) \log_{5}89 (b) \log_{\sqrt{2}}\ \sqrt{5}
Round answers to four decimal places.
(a) \log_{5}89={\frac{\log\,89}{\log5}}\approx \frac{1.9493900007}{0.6989700043}\\
\approx\,2.7889or
\log_{5}89={\frac{\ln89}{\ln5}}~~\approx \frac{4.48863637}{1.609437912}\\ \approx\,2.7889(b) \log_{\sqrt{2}}\,\sqrt{5}=\frac{\log\;\sqrt{5}}{\log\;\sqrt{2}}= \frac {{\frac{1}{2}}\log5\,}{{\frac {1}{2}}\log 2}\\
={\frac{\log5}{\log2}}\approx2.3219or
\log_{\sqrt{2}}\ \sqrt{5}=\frac{\ln\sqrt{5}}{\ln\sqrt{2}}\ =\frac {{\frac{1}{2}}\ln5\,}{{\frac {1}{2}}\ln 2}\\ ={\frac{\ln{\mathsf{5}}}{\ln{\mathsf{2}}}}\approx2.3219Related Answered Questions
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