Question

if log to the base 27 (log x to the base 3 ) = 1\3 then x=

Answer 1

Answer:

x= 3

Step-by-step explanation:

Rewrite

log

27

(

x

)

=

1

3

in exponential form using the definition of a logarithm. If

x

and

b

are positive real numbers and

b

≠

1

, then

log

b

(

x

)

=

y

is equivalent to

b

y

=

x

.

27

1

3

=

x

Answer 2

Concept

The properties of log are the rules of logarithms which are derived from the rules of exponent. These properties of logarithms are majorly used to solve the logarithmic equations and for simplification of logarithmic expression.

Properties of log

1. logₐ mn = logₐ m + logₐ n

2. logₐ m/n = logₐ m - logₐ n

3. logₐ mn = n logₐ m (power property)

Given

log₂₇(log₃x) = 1/3

Find

Value of x

Solution

Using Properties of logarithms

Property :

If logₙb = a

Then b = nᵃ

log₂₇(log₃x) = 1/3

log₃x = 27^(1/3)

log₃x = 3

x = 3³

x = 27

If, log₂₇(log₃x) = 1/3 then the value of x is 27.

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