SOLUTION: Let f(x) = cx^k. Suppose that f(5.4) is 5.8 times as large as f(1.92). What is the value of k? (Round your answer to two decimal places.)

Algebra ->  Rational-functions -> SOLUTION: Let f(x) = cx^k. Suppose that f(5.4) is 5.8 times as large as f(1.92). What is the value of k? (Round your answer to two decimal places.)      Log On


   

Question 760852: Let f(x) = cx^k. Suppose that f(5.4) is 5.8 times as large as f(1.92). What is the value of k? (Round your answer to two decimal places.)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
c%2A5.4%5Ek=5.8%2Ac%2A1.92%5Ek is the direct translation of the description.

Notice you can divide left and right sides by c.
5.4%5Ek=%285.8%291.92%5Ek

Logarithms of both sides will be equal.
log%28%285.4%5Ek%29%29=log%28%285.8%2A1.92%5Ek%29%29

As an approach, using base of 10 and ...
k%2Alog%2810%2C5.4%29=log%2810%2C5.8%29%2Bk%2Alog%2810%2C1.92%29
k%28log%2810%2C5.4%29-log%2810%2C1.92%29%29=log%2810%2C5.8%29
highlight%28k=%28log%2810%2C5.8%29%29%2F%28log%2810%2C5.4%29-log%2810%2C1.92%29%29%29

Finish by either table of logarithms or scientific calculator.

k=0.7634%2F%280.7324-0.2833%29
highlight%28k=1.70%29