Question

Will give medal. Please explain

Answer 1

Consider the equation
\[a^b=b\]
, where a and b are different numbers.

What is the value of a? Enter your answer on the first line.

What is the value of b? Enter your answer on the second line.

Answer 2

@Jhannybean

Answer 3

@SolomonZelman

Answer 4

\(\large\color{black}{ a^b=b }\)

\(\large\color{black}{ \ln(a^b)=\ln(b ) }\)

\(\large\color{black}{ b\ln(a)=\ln(b ) }\)

\(\large\color{black}{ \ln(a)=\frac{1}{b}\ln(b ) }\)

\(\large\color{black}{ \ln(a)=\ln(\sqrt[b]{b} ) }\)

\(\large\color{black}{ a=\sqrt[b]{b} }\)

Answer 5

I found a in term of b.

Answer 6

ok. What does In stand for?

Answer 7

I can't do otherwise, because there are 2 unknowns in 1 equation.
kln is a natural log.

Answer 8

ln is a natural log.

Answer 9

ok

Answer 10

you could have just used log, it wouldn't make any difference.

Answer 11

I am again making it too complicated.

Answer 12

I have to use numbers though