Consider the system of equations log3⁡log2⁡x+log1/3⁡log1/2⁡y=1 and xy2=9The value of x lies in the intervalThe value of  1/y lies in the interval

log3⁡log2⁡x+log1/3⁡log1/2⁡y=1⇒ log3⁡log2⁡x−log3⁡−log2⁡y=1⇒ log3⁡−log2⁡xlog2⁡y=1⇒ −log2⁡xlog2⁡y=3⇒ xy3=1 Also, xy2=9⇒ y=19∴ x=729 log3⁡log2⁡x+log1/3⁡log1/2⁡y=1⇒ log3⁡log2⁡x−log3⁡−log2⁡y=1⇒ log3⁡−log2⁡xlog2⁡y=1⇒ −log2⁡xlog2⁡y=3⇒ xy3=1 Also, xy2=9⇒ y=19∴ x=729