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]
