Question

Two experiments were carried out to obtain a relationship between the variables x and y. Equations $3(9^{x} )=27^{y}$ and $log_{2}y = 2+ log_{2} (x-2)$ were obtained from the first and second experiment respectively. Find the values of x and y that satisfy both the experiments.


Can anyone help me with this question please

Answer 1

Answer:

x = 5/2

y = 2

For explaination , please refer to the attachment .

Note:

★ log_b ( N ) = a => N = b^a

★ log(a×b) = log( a ) + log( b )

★ log(a/b) = log( a ) - log( b )

★ logNⁿ = n×logN

★ log_bⁿ ( N ) = (1/n)×log_b ( N )

★ log_b ( a ) = 1 / log_a ( b )

★ log_b ( a ) = [log_b ( k )]×[log_k ( a )]

★ log_b ( b ) = 1

★ log 1 = 0