Question

How does expression written in exponential form: 6^log6(x) turn to a logarithm form: 6^log6(x)=x? HELP!

Answer 1

M textbook says,

6^log6(x) = y
log6(y) = log6(x)
y=x
6^log6(x)=y

How did they get from 6^log6(x)=y to log6(y) = log6(x)?

Answer 2

Do you mean
\(^6\log(6x)=y\)?

Answer 3

no, \[6^{\log6x}\]

Answer 4

And log6(x) is logx with base 6 or log(6x) with base 10?

Answer 5

logx with base 6

Answer 6

Then it's the definition of logarithm.
if 3^2=9 then log_3(9)=2.
6^log_6(x)=y; say log_6(x)=a
6^a=y then log_6(y)=a
log_6(y)=log_6(x)

Answer 7

In general, a^b=c implies log_a(c)=b