solve for the unknown 216=36^3x

Question

stormfire1 · Answer

Is that $$36^3x$$ or $$36^{3x}$$

anonymous · Answer

second choice

anonymous · Answer

$$6^3=(6^2)^{3x}$$ is a start

stormfire1 · Answer

Danyel, do you understand it from there?

anonymous · Answer

I guess not because when I put that in I end up with a decimal.

anonymous · Answer

My book doesnt even tell me how to do this.

stormfire1 · Answer

On the left you have 6^3 and you need to make the right equal that.  

On the right, you have $$(6^2)^{3x}$$.  Using the rules of exponents, you should see that this is an exponent raised to an exponent.  That means you need to multiply the exponents together and ultimately they should = the "3" that's on the left side of the equation.

2 * 3x = 3

x must be 1/2

anonymous · Answer

why won't it be 6 because 2*3=6

stormfire1 · Answer

x = 1/2 so:
2 * 3 * 1/2 = 3

anonymous · Answer

ok that makes sense

anonymous · Answer

glad I asked

stormfire1 · Answer

You can of course check your answer using a calculator and plugging in 1/2 for x in the original equation.  You'll see that it = 216

anonymous · Answer

so when I write out the answer I will write x=1/2?

stormfire1 · Answer

Yes

anonymous · Answer

I think I am starting to understand a bit better. thank you

stormfire1 · Answer

glad to help