### Logarithms.

is the inverse function to exponentation, as it answers the question, how many of one number do we multiply to get another number.
If log_b a = x then a = b^x

Subjects > Mathematics > Logarithms

Question 05:

Find the value of log root(3)(1/27)

###### Solution:
Given,
log root(3)(1/27)
But we know that
root(n)(x) = x^(1/n)

Hence,
⇒ log (1/27)^(1/3)
but 27 = 3^3
⇒ log (1/(3^3))^(1/3)

But also,
1/(3^3) = (1/3)^3
Hence,
⇒ log (1/3)^(3 * 1/3) = log (1/3)
⇒ log (1/3) = log 3^-1 = -log 3
From mathematical table,
log 3 ~~ 0.4771
Hence,
⇒ -log 3 = -0.4771
∴ log root(3)(1/27) ~~ -0.4771

Sorry, it's under construction !

Sorry, it's under construction !

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Question 05:

Find the value of log root(3)(1/27)

###### Solution:
Given,
log root(3)(1/27)
But we know that
root(n)(x) = x^(1/n)

Hence,
⇒ log (1/27)^(1/3)
but 27 = 3^3
⇒ log (1/(3^3))^(1/3)

But also,
1/(3^3) = (1/3)^3
Hence,
⇒ log (1/3)^(3 * 1/3) = log (1/3)
⇒ log (1/3) = log 3^-1 = -log 3
From mathematical table,
log 3 ~~ 0.4771
Hence,
⇒ -log 3 = -0.4771
∴ log root(3)(1/27) ~~ -0.4771

Sorry, it's under construction !

Sorry, it's under construction !

Skills covered in the above question

Related Lessons