[Question]
Is log_3(5) equal to log_5(3)? Explain your answer. Do not evaluate
the logarithms.
[Difficulty]
I'm not sure if my answer is sufficient/detailed enough to properly
explain why these two logarithms are not equal.
[Thoughts]
log_3(5) is not equal to log_5(3).
Using the change of base formula log_3(5) becomes log(3)/log(5) and
log_5(3) becomes log(5)/log(3).
let log_3(5)=x 3^x=5 x>1
let log_5(3)=y 5^y=3 y<1
Therefore x does not equal y and log_3(5) is not equal to log_5(3).
Since the quotients aren't equivalent, the logarithms are not equal.
In general log_a(b) is not equal to log_b(a).
Are my thoughts/answer true?
Is log_3(5) equal to log_5(3)? Explain your answer. Do not evaluate
the logarithms.
[Difficulty]
I'm not sure if my answer is sufficient/detailed enough to properly
explain why these two logarithms are not equal.
[Thoughts]
log_3(5) is not equal to log_5(3).
Using the change of base formula log_3(5) becomes log(3)/log(5) and
log_5(3) becomes log(5)/log(3).
let log_3(5)=x 3^x=5 x>1
let log_5(3)=y 5^y=3 y<1
Therefore x does not equal y and log_3(5) is not equal to log_5(3).
Since the quotients aren't equivalent, the logarithms are not equal.
In general log_a(b) is not equal to log_b(a).
Are my thoughts/answer true?