Find each logarithm below without using a calculator.

Question

anonymous · Answer

$$\log_{3} 3^{6}$$

anonymous · Answer

and $$10^{\log9 }$$

anonymous · Answer

Remember that:
$$x = \log_{b}b^{x}$$

anonymous · Answer

I dont know how to do these at all so this will probably be painful for you and I'm sorry in advance...

anonymous · Answer

Not a problem.  Take a look at the formula I posted again.

When your base equals your number, it equals the power to which your number is raised.

anonymous · Answer

In other words, when you have $\log_{b} (b)^{x}$, the answer is simply $x$.

anonymous · Answer

So in my first one, the answer would just be 6?

anonymous · Answer

That's right.

anonymous · Answer

You can try it in a calculator if you want to confirm.  But now, if you're given another question like that, you can do it without one.  This is where "knowing the rules" comes in handy.

anonymous · Answer

Well that is easy...

anonymous · Answer

I feel kinda dumb now...

anonymous · Answer

No, don't feel dumb!

anonymous · Answer

So the second one would be 9

anonymous · Answer

Right!  Same rule applies.

$$\large{b^{\log_{b}x}} = x$$

anonymous · Answer

Okay awesome! Thanks a lot, now onto posting the next one lol...I'll see if I can puzzle it out first though.

anonymous · Answer

No problem!  Sure: post it, then try to solve it.