If a^x=b, then x=? I couldn't remember nor find information by googling on how to find the exponent of a that gives b as the result. If a^x=b, then x=log_a b but how do you find x?

caritatsjq

caritatsjq

Answered question

2022-10-12

If a x = b, then x = l o g a b but how do you find x?

Answer & Explanation

Claire Love

Claire Love

Beginner2022-10-13Added 14 answers

For a , b > 0,  using the two sides of the equation, get the regular logarithm.
a x = b becomes ln  a x = ln  b 
That is x ln  a = ln  b
Or x = ln  b ln  a 

Kevin Charles

Kevin Charles

Beginner2022-10-14Added 4 answers

The method that sticks in my mind the best is to multiply both sides by a logarithm (any base log will do):
b = a x    ln  ( b ) = ln  ( a x ) = x ln  ( a )
If ln  ( a )  0 then
x = ln  ( b ) ln  ( a ) 

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