Asked by sunkanmi
5^(logx) + x^(log5) = 50 . Find x
Answers
Answered by
Steve
5^(logx) + x^(log5) = 50
Note that
log(5^logx)) = logx * log5
log(x^log5)) = log5 * logx
So, the two are equal. That means
2*5^logx = 50
5^logx = 25 = 5^2
logx = 2
x = b^2
where logs are base b.
So, if natural logs, x = e^2
if common logs, x = 10^2 = 100
check (common logs):
5^log100 + 100^log5 = 50
5^2 + 10^log25 = 50
25 + 25 = 50
Note that
log(5^logx)) = logx * log5
log(x^log5)) = log5 * logx
So, the two are equal. That means
2*5^logx = 50
5^logx = 25 = 5^2
logx = 2
x = b^2
where logs are base b.
So, if natural logs, x = e^2
if common logs, x = 10^2 = 100
check (common logs):
5^log100 + 100^log5 = 50
5^2 + 10^log25 = 50
25 + 25 = 50
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.