Question

If x = 27, y = log3 4 then x^y​

Answer 1

Answer:

27^log[3](4) =>

(3^3)^log[3](4) =>

3^(3 * log[3](4)) =>

3^log[3](4^3) =>

4^3 =>

64

Step-by-step explanation:

Answer 2

Answer:

Required value is 64.

Step-by-step explanation:

This is a problem of logarithm. By power rule of logarithms we can solve this.

Given,

$x = 27 \: \: and \: \: y = log_{3}(4)$

Now ,

${x}^{y} = {27}^{ log_{3}(4) } = { {3}^{3} }^{ log_{3}(4) } = {3}^{3 \times log_{3}(4) } = {3}^{ log_{3}( {4}^{3} ) } = {4}^{3} = 64$

Required value is 64.

Here applied formulas are,

$log_{x}( {y}^{a} ) = a log_{x}(y)$

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

${x}^{ {y}^{a} } = {x}^{ya}$