Question

# 3. (1) hog6471 - log64y2 = 215 (D) logo (122 ) 13 81logs 9 + 3 log 3 Let N = 9257 - 12510g2s 6. Which of the following 409 (A) N is prime (B) N is rational (C) N is coprime with every other natural number (D) log2N is an ev nich of the following statements(s) Islare correct (D) log2N is an even number hold good?

Solution

$N=\frac{81{\displaystyle \frac{1}{{\mathrm{log}}_{5}9}}+3{\displaystyle \frac{3}{\mathrm{log}\sqrt{6}3}}}{409}\left({\sqrt{7}}^{\frac{2}{{\mathrm{log}}_{25}7}-{{125}^{\mathrm{log}}}_{25}6}\right)\phantom{\rule{0ex}{0ex}}=\frac{{\mathrm{log}}_{{5}^{5}}}{{\mathrm{log}}_{5}9}+3\frac{\mathrm{log}{\sqrt{6}}^{\left(6\right)3/6}}{\mathrm{log}{\sqrt{6}}^{3}}\left(\frac{{{{\mathrm{log}}_{25}}^{25}}^{2}}{{}_{\sqrt{7}}{{\mathrm{log}}_{25}}^{7}-}{125}^{{{\mathrm{log}}_{25}}^{6}}\right)\phantom{\rule{0ex}{0ex}}=\frac{81{{\mathrm{log}}_{9}}^{5}+3{{\mathrm{log}}_{3}}^{{\left(6\right)}^{3/2}}}{409}\left[{\left(\sqrt{7}\right)}^{{\mathrm{log}}_{7}{25}^{2}}-{(5}^{}\right]$