Question about inequality and logarithms Let's say we have an inequality: x<y does this hold true? log x<log y and if so, how can I prove it?

Nico Patterson

Nico Patterson

Answered question

2022-11-13

Question about inequality and logarithms
Let's say we have an inequality:
x < y
does this hold true?
log x < log y
and if so, how can I prove it?

Answer & Explanation

Rebecca Benitez

Rebecca Benitez

Beginner2022-11-14Added 20 answers

Hint: f ( x ) = log a ( x ) f ( x ) = 1 ln ( a ) x
Howard Nelson

Howard Nelson

Beginner2022-11-15Added 6 answers

Let log B x = a and log B y = b for B > 0. Then x = B a and y = B b . So we can write
x < y B a < B b .
If 0 < B 1, then
B a < B b a > b log B x > log B y
but otherwise (say B > 1),
B a < B b a < b log B x < log B y

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?