Question

find the log
log1/3^(81)​

Answer 1

Answer:

Rewrite as an equation.

log1/3(81)=x in exponential form using the definition of a logarithm. If x and b are positive real numbers and bdoes not equal.

1, then log b(x)=y is equivalent to by=x.

.(1/3)x=81

Create expressions in the equation that all have equal bases.

(3−1)x=34

=34

Rewrite

(3−1)x as 3−x.

3-x=34

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

−x=4

Solve for x.

x=−4

The variable x is equal to −4.

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Answer 2

Answer:

log 1/3^ 81

===> ( 81 )^x = 1/3

===> ( 3^4)^x = 3^1

[ ( a^m ) ^ n = a ^ m + n ]

===> 3^4x = 3^1

Here , if the bases are equal then their exponents are also equal

4x = 1

x = 1/4

log^3 to the base of 81 = 1/4