Question

If x=81 and y=log 4 to the base 3 then find the value of x power y.

Answer 1

hey arpana here is your answer.

Theory:
${y}^{ log_{n}(x) } ={x}^{ log_{n}(y) }$

Solution:
$x = 81 \\ y = log_{3}(4)$
${x}^{y} = {81}^{ log_{3}(4) } = {4}^{ log_{3}(81) } = {4}^{ log_{3}( {3}^{4} ) } = {4}^{4 log_{3}(3) } = {4}^{4} = 256$
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Answer 2

Step-by-step explanation:

Theory:

{y}^{ log_{n}(x) } ={x}^{ log_{n}(y) }y

log

n

(x)

=x

log

n

(y)

Solution:

\begin{gathered}x = 81 \\ y = log_{3}(4) \end{gathered}

x=81

y=log

3

(4)

{x}^{y} = {81}^{ log_{3}(4) } = {4}^{ log_{3}(81) } = {4}^{ log_{3}( {3}^{4} ) } = {4}^{4 log_{3}(3) } = {4}^{4} = 256x

y

=81

log

3

(4)

=4

log

3

(81)

=4

log

3

(3

4

)

=4

4log

3

(3)

=4

4

=256

hope you like it..

please mark me brainliest if you found it useful.