solve for x.
1/27=9^7x+3

Question

stormfire1 · Answer

$$x=\frac{\frac{1}{27}-3}{9^7}$$

anonymous · Answer

x= (-9/14)

stormfire1 · Answer

How did you get that?

anonymous · Answer

3^(-3)=3^2*(7x+3)
3^(-3)=3^(14x+6)
this implies that
-3=14x+6
i.e., 14x= -6-3
x=-9/14

precal · Answer

Stormfire 1 is wrong
Sheg is correct

stormfire1 · Answer

Still not seeing it...I see the original equation as:$$\frac{1}{27}=9^7x+3$$$$3^{-3}-3=9^7x$$$$x=\frac{3^{-3}+3}{9^7}$$Maybe I'm reading the original equation differently...

precal · Answer

The rule is you can log both sides or unlog both sides.
You also, can take the powers and set them equal to each other.
9 can be written with the base of 3 just like you wrote 3 to the negative 3 power.
Besides your x value does not match sheg's x value.
You should be able to sub your x value back into the equation in order for it to be true.
Your x value does not work.

stormfire1 · Answer

I'm aware of the log & exponent rules :)  As you can see from my post, I read the original equation differently.  I will admit that I flipped a sign in the equation editor by mistake in my last post...which may have thrown you off.  My original post did have the correct answer for the problem as I read it:

$$\frac{1}{27}=9^7x+3$$
However, sheg reads it as: $$\frac{1}{27}=9^{7x+3}+3$$which explains the different answers.  

The bottom line is that a few parentheses in the original question would have made everything more clear :)