Logarithm equations It has been years since I had to take a math course. I am currently in an advanced Computer Science course and I have been hit with a hw assignment that is bringing back all the math I used to crank out. Can someone help me understand this question? Show that log_a x=c log_b x for some constant c (expressed only in terms of the constants a and b).

Jaelyn Payne

Jaelyn Payne

Answered question

2022-10-16

Logarithm equations
It has been years since I had to take a math course. I am currently in an advanced Computer Science course and I have been hit with a hw assignment that is bringing back all the math I used to crank out.
Can someone help me understand this question?
Show that log a x = c log b x for some constant c (expressed only in terms of the constants a and b).

Answer & Explanation

Immanuel Brennan

Immanuel Brennan

Beginner2022-10-17Added 9 answers

Hint:
log a x = ln x ln a , for any x , a > 0 ( a 1).
Kevin Charles

Kevin Charles

Beginner2022-10-18Added 4 answers

If I understood your question correctly:
log a x = c log b x     c = log a x log b x
By the law of logarithm, log a b = 1 log b a
Therefore,
c = log x b log x a = log a b
In the last line, I used the following result (change of base to x):
log k h = log p h log p k

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