Question

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

• A. $25/2$
• B. $25/4$
• C. $25/3$
• D. None of these

Answer 1

The correct option is A $25/2$

${49}^{(1-{\log }_{7}2)}+5^{-{\log }_{5}4}$
${\left({\left(7\right)}^2\right)}^{(1-{\log }_{7}2)}+5^{-{\log }_{5}4}$
$7^{2(1-{\log }_{7}2)}+5^{-{\log }_{5}4}$
$7^{2-2{\log }_{7}2}+\frac{1}{5^{{\log }_{5}4}}$
$7^2.7^{-2{\log }_{7}2}+\frac{1}{4}$
$49\left(\frac{1}{7^{{\log }_7{\left(2\right)}^2}}\right)+\frac{1}{4}$
$49\left(\frac{1}{2^2}\right)+\frac{1}{4}$
$49\left(\frac{1}{4}\right)+\frac{1}{4}$
$\frac{49}{4}+\frac{1}{4}=\frac{50}{4}$
$=\frac{25}{2}$