Possible book error

Question

I am a math hobbyist who is stuck.

My understanding is that when we have a log raised to a power, we bring it to the front of the computation.

(log4.1)^2.4 = 2.4 Log 4.1 = 1.47

The book is giving as the proper answer to that computation as .309 which requires that the log of 4.1 (.6127) be actually raised to the power of 2.4 (...an easy error to make if indeed the book is wrong.)

Log 4.1 raised to the 2.4 power = .309

Stated differently: The book is giving .309 as the answer to this computation. That is, the book is raising the log to the power as the correct process rather than bringing 2.4 in front of the log. Can this be correct?

The only way I can get the book answer (.309) is by actually raising .6127 to the 2.4 power.

Answer 1

Ron,

Actually, the book is right.

This may be the source of the misunderstanding:

log(a^b) = b log a

but

(log a)^b is different, because

it does indeed mean that you take the log of a, and raise it to the b power. So, if you want to bring the b forward you’ve got to take log again.

log ( (log a)^b ) = b log (log a)