+0

# Help Please!!!

+9
165
2
+1070

Simplify

Apr 4, 2020

### 2+0 Answers

#1
+10801
+1

Simplify

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

Hello SpongeBobRules24!

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

$$=3\cdot a+b-c-d=6.04158747083$$

$$9^a=18$$                           $$a=2.631$$

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

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

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

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

!

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