49-log-7-6-log-3-5-log-2-3-log-5-2-

Question Number 122286 by ZiYangLee last updated on 15/Nov/20

{(49^{\log_{7} 6})}^{\log_{3} 5^{\log_{2} 3^{\log_{5} 2}}} = ?

Answered by TANMAY PANACEA last updated on 15/Nov/20

{(49^{{l o g}_{7}^{6}})}^{{l o g}_{3} 5^{{l o g}_{2} 3^{{l o g}_{5} 2}}}

{(49^{a})}^{b^{\frac{l n 2}{l n 5} \times \frac{l n 3}{l n 2}}}

{(49^{a})}^{b^{\frac{l n 3}{l n 5}}}

{(49^{a})}^{\frac{l n 5}{l n 3} \times \frac{l n 3}{l n 5}}

49^{a} = p

{l n}_{49} p = a

\frac{l n p}{2 l n 7} = a = \frac{l n 6}{l n 7}

l n p = 2 l n 6 = l n 6^{2}

p = 36