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