Question

Log(logx) by product rule ?

Answer 1

Answer:

When b is raised to the power of y is equal x:

b y = x

Then the base b logarithm of x is equal to y:

logb(x) = y

For example when:  

24 = 16  

Then  

log2 (16) = 4

Logarithm as inverse function of exponential function

The logarithmic function,  

y = logb(x)  

is the inverse function of the exponential function,  

x = b^y  

So if we calculate the exponential function of the logarithm of x (x>0),  

f (f -1(x)) = blogb(x) = x  

Or if we calculate the logarithm of the exponential function of x,  

f -1(f (x)) = logb(bx) = x

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