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avatar+1088 

Simplify

 Apr 4, 2020
 #1
avatar+9477 
+1

Simplify

 \(3log_9(18)+log_3(\sqrt{\frac{8}{27}})-log_{\frac{1}{27}}(81)-log_{\sqrt{3}}(2\sqrt{2}) \)

 

Hello SpongeBobRules24!

 

\(3log_9(18)+log_3(\sqrt{\frac{8}{27}})-log_{\frac{1}{27}}(81)-log_{\sqrt{3}}(2\sqrt{2}) \)

\(=3\cdot a+b-c-d=6.04158747083\)

 

\(9^a=18\)                           \(a=2.631\)

\(3^b=\sqrt{\frac{2^3}{3^3}}=(\frac{2}{3})^{\frac{3}{2}}\)        \(b=-0.5536\)

\((\frac{1}{27})^c=81\)                      \(c=-\frac{4}{3}\)

\((\sqrt{3})^d=3\sqrt{2}\)                 \(d=2.6309\)

 

\(3log_9(18)+log_3(\sqrt{\frac{8}{27}})-log_{\frac{1}{27}}(81)-log_{\sqrt{3}}(2\sqrt{2}) = 6.04158747083\)

laugh  !

 Apr 4, 2020
edited by asinus  Apr 4, 2020
edited by asinus  Apr 4, 2020
 #2
avatar
+1

simplify | 3 log(9, 18) + log(3, sqrt(8/27)) - log(1/27, 81) - log(sqrt(3), 2 sqrt(2))

 

4/3 - (3 log(3/2))/(2 log(3)) - (3 log(2))/log(3) + (3 log(18))/log(9)

 

log(33853318889472)/log(729) - log(8)/log(3)

 

= 17 / 6

 Apr 4, 2020

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