Solve the inequality 10 l 10n - 8 l

The first step is to simplify the given expression,
dividing it by 10 both sides:

10|10n -
8|<80

|10n -
8|<8

Now, we'll discuss the absolute value of the
expression 10n - 8:

Case 1) 10n - 8 for 10n -
8>=0

10n>=8

n>=8/10

n>=4/5

We'll
solve the inequality:

10n - 8 <
8

10n < 16

n <
16/10

n <
1.6

The interval of admissisble value of n,
for this situation,  is [4/5 , 1.6).

Case 2)
8 - 10,  for 10n -
8<0

n<4/5

We'll
solve the inequality:

8 - 10n <
8

-10n < 0

10n >
0

n >
0

The interval of admissible values for n,
for this case, is (0 , 4/5).