Logarithms

Question

log(log(10000^25x))

Answer 1

This is composition of functions.  Evaluate the inner function first.

 

log(10000^25x)

 

 

The exponent becomes the coefficient of the log.

 

 

25x(log10000) =

 

4(25x) = 100x

 

 

Next, evaluate the outer function.

 

log(log(10000^25x)) =

 

log(100x)

 

 

log(100x) is a product of logs.

 

 

log(100) + log(x) =

 

2 + log(x)

 

Answer 2

log(log(10000^25x)) = log[25xlog(10000)]

 

                                   = log[25xlog(10⁴)]

 

                                   = log[25x(4)]

 

                                   = log(100x)

 

                                   = log100 + logx = 2 + logx