Solve 3 log6 2 + 2 log6 3 - log6 x = 2

Question 10 options:
1) x = 2
2) x = 6
3) x = 15
4) x = 36

Question

Solve 3 log6 2 + 2 log6 3 - log6 x = 2

Question 10 options:
	1)	x = 2
	2)	x = 6
	3)	x = 15
	4)	x = 36

dumbcow · Answer

x=2

anonymous · Answer

The trick for solving all types of logarithms are using and memorizing the properties. Therefore four properties we are going to use for this exercise is as follows:$$\log_{A}B+\log_AC=\log_AB*C$$;$$\log_{A}B-\log_AC=\log_A(B/C)$$ ; $$\log_AB ^{C}=C*\log_AB$$ and finally $$A ^{\log_AB}=B$$. Now that you know the basic rules, lets apply them for this particular exercise:
$$3\log_{6}2+2\log_63-\log_6x=2$$ can be simplified using the third property as$$\log_62^{3}+\log_63^{2}-\log_6x=2$$ which can simplify by the first property$$\log_6(2^{3}*3^{2})-\log_6x=2$$  and by the second as$$\log_6{((8*9)/x)=2}$$. Using the fourth property we have that:$$6^{\log_{6}(72/x)}=6^{2}$$ which gives us$$72/x = 36$$ that simplifies into$$x=72/36=2$$. Peace, Love and Happiness from Puerto Rico