Fill the missing values to make the equations true.

Question

asked Nov 25, 2022 33.2k views

1 Answer

SubqueryCrunch · Answer 1 · 2022-11-30T21:14:53+0000

Answer:

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) ,
$\log_(c) a^(b)$

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

$-\log_(7) 81$

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

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