Inequality ((17)/(25))^k <= 10^(-5)

Deja Bradshaw 2022-10-13 Answered
Inequality ( 17 25 ) k 10 5 - Solve for k
How can I solve for k the following inequality :
( 17 25 ) k 10 5
This is what I got so far. By taking log k from both sides I get:
log k ( 17 25 ) k log k 10 5
How can I continue from here?
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Answers (2)

Kristin Myers
Answered 2022-10-14 Author has 12 answers
Using the natural logarithm instead:
k ln 17 25 5 ln 10
Note that ln 17 25 < 0 since 17 25 < 1, so by dividing both sides you'll get the equivalent inequality
k 5 ln 10 ln 17 25 = 5 ln 10 ln 25 17 = 5 log 25 17 10.
(where the inequality has been flipped, since as noted above we divide both sides by a negative number).
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tikaj1x
Answered 2022-10-15 Author has 4 answers
( 17 25 ) k 10 5 k ln ( 17 25 ) 5 ln ( 10 ) k ln ( 25 17 ) 5 ln ( 10 ) k 5 ln ( 10 ) ln ( 25 17 ) k 29.85
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