Exponential function leads to unsolvable logarithm. Problem: f(t)=0.75∗10:(kt) where k is a constant. We know that f(2)=3. Find f(3).

ajakanvao

ajakanvao

Answered question

2022-11-05

Exponential function leads to unsolvable logarithm.
Problem: f ( t ) = 0.75 10 k t where k is a constant. We know that f ( 2 ) = 3. Find f ( 3 )
My approach:
Rewrite f ( 2 ) as: 0.75 10 2 k = 3
Try to solve for k, eliminate 0.75 first: 10 2 k = 4
This is where I get stuck: l o g 10 4 = 2 k
Where do I go from there? Am I doing something wrong? The answer is supposed to be f ( 3 ) = 6  
Edit: typo in the logs, fixed. And I solved it, thanks everyone!

Answer & Explanation

Prezrenjes0n

Prezrenjes0n

Beginner2022-11-06Added 19 answers

The statement 10 2 k = 4 doesn't imply 2 k = log 4 ( 10 ); it implies 2 k = log 10 ( 4 ). So, you have that
k = log 10 ( 4 ) 2 ,
and therefore
f ( 3 ) = 3 4 10 3 log 10 ( 4 ) / 2 .
Your task now is to use the laws of logarithms/exponentials to simplify this expression.

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