Solve. (1/36)= 6^(x-3)

A) x = -5
B) x = - 3/2
C) x = 7/2
D) x = 1

Question

Solve. (1/36)= 6^(x-3)

A) x = -5
B) x = - 3/2
C) x = 7/2
D) x = 1

anonymous · Answer

Hint: ln both sides first in order to bring down (x-3)

anonymous · Answer

ln= natural log

anonymous · Answer

I'm not sure if bringing logs into this is entirely necessary.
$$1/36 = 6^{-2}$$
If you subtract that from both sides you get 
$$0=6^{x-3}-6^{-2}$$
There's gotta be some way to solve for x from there, I just can't think of it right now.

anonymous · Answer

You have to use natural log. That or you just plug in values until you find the right one.

anonymous · Answer

try $\frac{1}{36}=6^{-2}$

anonymous · Answer

no logs involved 
$$6^{-2}=6^{x-3}\iff -2=x-3$$

anonymous · Answer

solve for $x$ in one step by adding 3 to both sides of 
$$-2=x-3$$ to get 
$$x=1$$

anonymous · Answer

Aha, that's right. I remember now =)
If the bases are the same, you can set the exponents equal to each other.

anonymous · Answer

I think it's better to get people use to solving natural logs. It's only going to get more complicated further down the road.