`log_5 (1/125)` Find the exact value of logarithmic expression without using a calculator. (If this is not possible, then state the reason.)

Textbook Question

Chapter 3, 3.3 - Problem 22 - Precalculus (3rd Edition, Ron Larson).
See all solutions for this textbook.

1 Answer | Add Yours

loves2learn's profile pic

loves2learn | (Level 3) Salutatorian

Posted on

`log_5(1/125)=x ` 
Rewrite log5 1/125 :

`1/125=125^-1 ` 
This gives:

 

`log_5(125^-1) ` , bring down the power

`-1(log_5(125)) ` , rewrite 125 in term of power of 5

`-1(log_5(5^3)) ` , again bring down the power

`(-1*3)(log_5(5)) ` , note `log_5(5)=1 ` 
Answer: `x = -3 `

We’ve answered 318,915 questions. We can answer yours, too.

Ask a question