Question 4.4.5.5: Writing a logarithmic Expression as a Sum and Difference of ......
Writing a logarithmic Expression as a Sum and Difference of Logarithms
Write
\log_{a}\frac{\sqrt{x^{2}+1}}{x^{3}(x+1)^{4}},\;\;\;x\gt 0as a sum and difference of logarithms. Express all powers as factors.
\log_{a}\frac{\sqrt{x^{2}+1}}{x^{3}(x+1)^{4}}={log}_{a}\,\sqrt{x^{2}\,+\,1}\;- \mathrm{log}_{a}[\,x^{3}(x\,+\,1\,)^{4}\,] Property (4)
=\,\log_{a}{\sqrt{x^{2}\,+\,1}}\,- \big[\log_{a}x^{3}+\,\log_{a}(x\,+\,1\,)^{4}\big] Property (3)
=\,\log_{a}(x^{2}\,+\,1\,)^{1/2} -\log_{a}\,x^{3}\,-\,\log_{a}(x\,+\,1\,)^{4}={\frac{1}{2}}\log_{a}(x^{2}+1)\ – 3\log_{a}x\,-\,4\log_{a}(x\,+\,1\,) Property (5)
Related Answered Questions
Question: 4.4.8.6
Verified Answer:
(a) The decay rate is |b|\,=\,|-0.0581|[/la...
Question: 4.4.8.5
Verified Answer:
(a) As t\rightarrow\infty.\;e^{-0.37t}\righ...
Question: 4.4.8.4
Verified Answer:
(a) Using formula (4) with T = 30 and u_{0}...
Question: 4.4.8.3
Verified Answer:
Using formula (3), the amount A of 14 present at t...
Question: 4.4.8.2
Verified Answer:
(a) Using formula (2), the number N of cells at ti...
Question: 4.4.8.1
Verified Answer:
(a) The intial amount of bacteria, N_{0}[/...
Question: 4.4.5.6
Verified Answer:
(a) \log_{a}7\,+\,4\log_{a}3\,=\,\log_{a}7\...
Question: 4.4.9.3
Verified Answer:
(a) See Figure 54 for a scatter diagram of the dat...
Question: 4.4.5.7
Verified Answer:
Remember, \log_{2}7 means “2 raised...
Question: 4.4.5.8
Verified Answer:
(a) \log_{5}89={\frac{\log\,89}{\log5}}\app...