Question

Clue #2: The Circle of LogsOur suspect journeyed into the jungle for the next crime. The King of the Jungle called a meeting of all the animals in his kingdom and ordered them to try and stop the suspect from killing all the jungle trees and interrupting the Circle of Logs. Your job is to beat the suspect to the end of the log cycle and restore the final arrow so life as a seed begins again. Start at I, find the value of a and use it to advance through The Circle of Logs.Once you reach V, use all the variables you found solving I through IV and solve for e. Accomplish this and all the animals of the jungle will sing your praises! Solve for e

Answer 1

I. First we will find the value of a

$\log _3a=3$$\begin{gathered} (\log _3a)^3=3^3 \\ a=27 \end{gathered}$

II. Then we need to find b

$a^b=531441$

we substitute the value of a

$\begin{gathered} 27^b=531441 \\ \end{gathered}$

we apply natural logarithm on both sides

$\begin{gathered} \ln (27)^b=\ln (531441) \\ b\ln (27)=\ln (531441) \\ b=\frac{\ln (531441)}{\ln (27)} \\ b=4 \end{gathered}$

The value of b is 4

b=4

III.

$\log _4c=-2$

$(\log _4c)^4=\log _4(\frac{1}{16})$

$c=\frac{1}{16}$

IV.

$2^{-2d}=c$$2^{-2d}=\frac{1}{16}$

We will use the natural logarithm

$\begin{gathered} \ln (2^{-2d})=\ln (\frac{1}{16}) \\ -2d\ln (2^{})=\ln (\frac{1}{16}) \\ d=\frac{\ln (\frac{1}{16})}{-2\ln (2)} \\ d=2 \end{gathered}$

V.

Then for e

$\text{alog}_db^{3e}=864c$

Then we substitute

$27\text{log}_24^{3e}=864(\frac{1}{16})$

we simplify

$27\text{log}_24^{3e}=54$$\text{log}_24^{3e}=\frac{54}{27}$$\text{log}_24^{3e}=2$$\begin{gathered} (\text{log}_24^{3e})^2=2^2 \\ 4^{3e}=4 \\ 3e=1 \\ e=\frac{1}{3} \end{gathered}$

ANSWER

a=27

b=4

c=1/16

d=2

e=1/3