Question

Find the value of ${49}^{\left(1-{\log }_{7}2\right)}+5^{-{\log }_{5}4}.$

Answer 1

${49}^{(1-{\log }_{7}2)}+5^{-{\log }_{5}4}$

${49}^{{\log }_7\left(\frac{7}{2}\right)}+5^{{\log }_5{\left(4\right)}^{-1}}$

${\left(\frac{7}{2}\right)}^2+{\left(4\right)}^{-1}$

$\frac{49}{4}+\frac{1}{4}=\frac{50}{4}=\frac{25}{2}$