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how would you solve this:

12^x x 3^3x =18

12x x 33x = 18

 

 

thanks!

 Sep 10, 2018
edited by Guest  Sep 10, 2018
 #1
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Solve for x
3^(4 x) 4^x = 18

Factor out the common power x from the left hand side:
324^x = 18

Take the logarithm base 324 of both sides:
 x = 1/2

 Sep 10, 2018
 #2
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Since 12 = 22*3 we can write 12x*33x=18 as 22x*34x=21*32

 

Divide both sides by 21*32 to get 2(2x-1)*3(4x-2)=1 or 2(2x-1)*3(4x-2)=1 or

2(2x-1)*32(2x-1)=1 or (2*32)(2x-1) = 1 or 18(2x-1) = 1

 

Now the only way 18 to some power can equal 1 is if that power is zero. Hence 2x - 1 = 0

so x = 1/2

 Sep 10, 2018

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