Why does log(base 27) 3 = (1/3) ?

Question

I'm prepping for a midterm; I'll apreciate your help to help me get this concept which escapes me at the moment.

Answer 1

because 27^(1/3) =3
[the 1/3 power is the cube root]

in general log(base b) A = X when b^X = A

Answer 2

When you rewrite log(base 27) 3 = (1/3) as an exponential equation it becomes

27 ^ (1/3) = 3

Since 1/3 as an exponent means the cube root, the cube root of 27 is 3.

Answer 3

hope u remember this rule

log(base a) a = 1

so log(base 27)3 = log(base 27) 27^(1/3)

i just substituted 3 = 27^(1/3)

so now i have the base number and the log number the same so i move 1/3 before log to get

(1/3)log(base 27) 27 = (1/3) * 1 by the rule i stated

= 1/3

Answer 4

(a million/3)^2 - x = 27 -x = 27 - (a million/3)^2 x = (a million/3)^2 - 27 possibly you meant (a million/3)^(2 - x) = 27. for that reason, (a million/3)^(2 - x) = 27 (a million/3)^(2 - x) = (a million/3)^(-3) 2 - x = -3 -x = -5 x = 5

Answer 5

Logarithms are the inverses of exponents. So every logarithm is equal to an exponent.

log(base 27) 3 = (1/3)

Above the log is equal to (1/3), when we rewrite it in exponential form the (1/3) will be the exponent to which the base is raised.

3^(1/3) = 27.

It's not the easiest concept in the world to fully understand, but as long as you always come back to the fact that logarithms are exponents, it will help with logarithmic computations and rewriting them.

Answer 6

log(base27) 3 = 1/3


Log definition :

log(base b) x = y <=> b ^ y = x





log(base 27) 3 = 1/3

27 ^ 1/3 = 3 (by log definition)

(3^3 )^1/3 = 3

3 ^3/3 = 3

3^1 = 3

3 = 3 (equality is true)

Answer 7

Let's rewrite this as exponential form. This mean that
27^(1/3)=3
This is right beacause raise a number to one-third is like taking the cube root.
So what is the cube root of 27. The answer is three.

Answer 8

log(base b)(a) = c and a = b^c
so...
3 = 27^1/3 or the cubed root of 27 = 3.