Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
Answer:
a) [tex]\log_{9} 8 + \log_{9} 11 = \log_{9} 88[/tex]
b) [tex]\log_{7} 11 - \log_{7} 3 = \log_{7} \frac{11}{3}[/tex]
c) [tex]\log_{7}\frac{1}{81} = -4\cdot \log_{7} 3[/tex]
Step-by-step explanation:
Now we proceed to solve each case by appropriate rules for logarithms.
a) The following property shall be used: [tex]\log_{c} a +\log_{c} b = \log_{c} a\cdot b[/tex] ([tex]a = 8[/tex], [tex]b = 11[/tex], [tex]c = 9[/tex])
[tex]\log_{9} 8 + \log_{9} 11 = \log_{9} 8\cdot 11[/tex]
[tex]\log_{9} 8 + \log_{9} 11 = \log_{9} 88[/tex]
b) The following property shall be used: [tex]\log_{c} a - \log_{c} b = \log_{c} \frac{a}{b}[/tex] ([tex]a = 11[/tex], [tex]b = 3[/tex], [tex]c = 7[/tex])
[tex]\log_{7} 11 - \log_{7} 3 = \log_{7} \frac{11}{3}[/tex]
c) The following properties shall be used: [tex]\frac{1}{d} = d^{-1}[/tex], [tex]\log_{c} a^{b}[/tex]
[tex]\log_{7} \frac{1}{81} = \log_{7} 81^{-1}[/tex]
[tex]-\log_{7} 81[/tex]
[tex]-\log_{7} 3^{4}[/tex]
[tex]\log_{7}\frac{1}{81} = -4\cdot \log_{7} 3[/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.