Question

Fill the missing values to make the equations true.

Answer 1

a)
`\log_(9) 8 + \log_(9) 11 = \log_(9) 88`

b)
`\log_(7) 11 - \log_(7) 3 = \log_(7) (11)/(3)`

c)
`\log_(7)(1)/(81) = -4\cdot \log_(7) 3`

Explanation:

Now we proceed to solve each case by appropriate rules for logarithms.

a) The following property shall be used:
`\log_(c) a +\log_(c) b = \log_(c) a\cdot b` (
`a = 8`,
`b = 11`,
`c = 9`)

`\log_(9) 8 + \log_(9) 11 = \log_(9) 8\cdot 11`

`\log_(9) 8 + \log_(9) 11 = \log_(9) 88`

b) The following property shall be used:
`\log_(c) a - \log_(c) b = \log_(c) (a)/(b)` (
`a = 11`,
`b = 3`,
`c = 7`)

`\log_(7) 11 - \log_(7) 3 = \log_(7) (11)/(3)`

c) The following properties shall be used:
`(1)/(d) = d^(-1)`,
`\log_(c) a^(b)`

`\log_(7) (1)/(81) = \log_(7) 81^(-1)`

`-\log_(7) 81`

`-\log_(7) 3^(4)`

`\log_(7)(1)/(81) = -4\cdot \log_(7) 3`