How do you solve #2\cdot 3^ { 10x + 6} = 18#?

4 Answers
Jul 20, 2018

The solution is #=-2/5#

Explanation:

The equation is

#2*3^(10x+6)=18#

Dividing by #2#

#3^(10x+6)=18/2=9=3^2#

Therefore,

The exponents are equal

#10x+6=2#

#10x=2-6=-4#

Dividing by #10#

#x=-4/10=-2/5#

Jul 20, 2018

#x=-2/5#

Explanation:

#3^(10x+6)=9#

#log_(3)3^(10x+6)=log_(3)9#

#10x+6=2#

#10x=-4#

#x=-4/10#

#x=-2/5#

Jul 20, 2018

#x=-2/5#

Explanation:

Here ,

#2*3^(10x+6)=2*9#

#=>2*3^(10x+6)=2*3^2#

Dividing both sides by #2#

#(cancel2*3^(10x+6))/cancel2=(cancel2*3^2)/cancel2#

#=>3^(10x+6)=3^2#

#=>10x+6=2#

Adding both sides #(-6)#

#=>10x+6+(-6)=2+(-6)#

#=>10x=-4#

Dividing both sides by #10#

#=>x=-4/10=-(2xx2)/(2xx5)#

#=>x=-2/5#

#x=-0.4#

Explanation:

#2\cdot 3^{10x+6}=18#

#3^{10x+6}=18/2#

#3^{10x+6}=9#

#3^{10x+6}=3^2#

Comparing the powers on base #3# on both the sides we get

#10x+6=2#

#10x=2-6#

#10=-4#

#x=-4/10#

#x=-0.4#