if log3 729=x then x=?
Answers
Rewrite as an equation.
log
3
(
729
)
=
x
Rewrite
log
3
(
729
)
=
x
in exponential form using the definition of a logarithm. If
x
and
b
are positive real numbers and
b
does not equal
1
, then
log
b
(
x
)
=
y
is equivalent to
b
y
=
x
.
3
x
=
729
Create equivalent expressions in the equation that all have equal bases.
3
x
=
3
6
Since the bases are the same, the two expressions are only equal if the exponents are also equal.
x
=
6
The variable
x
is equal to
6
.
6
Concept:
The power to which a number must be increased in order to obtain additional values is referred to as a logarithm. The easiest approach to express enormous numbers is this manner. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms can also be represented as multiplication and division of logarithms.
"The exponent by which b must be raised to generate a" is defined as "the logarithm of a positive real number a with regard to base b, a positive real number and b≠1
⇒ bˣ= a logba=x
Given:
log₃ 729=x
Find:
Find the value of x
Solution:
log₃ 729=x
log₃ 3⁶ =x
6log₃ 3=x
x=6
Therefore, the value of x is 6
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