Question

81^(1/log 3 base 5)+27^log36base9+3^4/log 9 base 7 is equal to​

Answer 1

Here's your solution buddy

Answer 2

Answer:

81^(1/log 3 base 5)+27^log36base9+3^4/log 9 base 7 is equal to ​$841+\sqrt{7}$.

Step-by-step explanation:

• GIVEN:

$81^{\frac{1}{\log _{5} 3}}+27^{\log _{9} 36}+3^{\frac{1}{\log _{7} 9}}$

$\frac{1}{\log _{5} 3}=\log _{3}(5)$

$So:\\81^{\frac{1}{\log _{5} 3}}=\left(3^{4}\right)^{\log _{3}(5)}\\=3^{4 \log _{3}(5)}\\=\left(3^{\log _{3}(5)}\right)^{4}\\=5^{4}\\=625\log _{9} 36\\=\frac{\log _{3}(36)}{\log _{3}(9)}\\=\frac{\log _{3}(36)}{\log _{3}\left(3^{2}\right)}\\=\frac{\log _{3}(36)}{2}$.......................................................(1)

$27^{\log _{9} 36}=\left(3^{3}\right)^{\frac{\log _{3}(36)}{2}}\\=\left(3^{\log _{3}(36)}\right)^{\frac{3}{2}}\\=36^{\frac{3}{2}}\\=\left(6^{2}\right)^{\frac{3}{2}}\\=6^{3}\\=216..............................................................(2)\\\\\frac{1}{\log _{7} 9}\\=\log _{9}(7)=\frac{\log _{3}(7)}{2}\\\\So\\\\3^{\frac{1}{\log _{7} 9}}\\=3^{\frac{\log _{3}(7)}{2}}\\=\left(3^{\log _{3}(7)}\right)^{\frac{1}{2}}\\=7^{\frac{1}{2}}=\sqrt{7}$..........................................................(3)

Putting this all together:

$81^{\frac{1}{\log _{5} 3}}+27^{\log _{9} 36}+3^{\frac{1}{\log _{7} 9}}=625+216+\sqrt{7}=841+\sqrt{7}$