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

1 Answer

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loves2learn | (Level 3) Salutatorian

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`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 `