Question
5^(logx) + x^(log5) = 50 . Find x
Answers
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