Mike is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation.

Question

agent0smith · Answer

Any idea what the first step might be?

kidthatbro8 · Answer

i thought about creating equal bases...

kidthatbro8 · Answer

@agent0smith ??

agent0smith · Answer

Good try... can you get 37 and 12 to be equal bases? You might notice that 37 is prime...

kidthatbro8 · Answer

yeah. what do we do then?

agent0smith · Answer

You must have learned some other methods to solve these...

wolf1728 · Answer

How about taking logarithms of both sides?

kidthatbro8 · Answer

like, making them both into logarithms?

wolf1728 · Answer

Yes, do you know how to do that?

kidthatbro8 · Answer

yes,, the formula is y = b^x <---> x = logb y

kidthatbro8 · Answer

so would it be something like x = log37 12? or is that wrong?

wolf1728 · Answer

Here's how I'd do it
37^x = 12
Taking logs of both sides
x * log (37) = log (12)
x = log (12) / log (37)
I think you can figure it out from there.

kidthatbro8 · Answer

uh, i don't think i know how to work it out from there, could you help me?

wolf1728 · Answer

Sure
Log (37) = 1.5682017241
Log (12) = 1.079181246

So x = 1.079181246 / 1.5682017241

x = 0.6881648129

To check that out do you have a calculator that can calculate 37^0.6881648129 ?

kidthatbro8 · Answer

my calculator says it's 11.9999999996

wolf1728 · Answer

Pretty darned close to 12 isn't it ? :-)

kidthatbro8 · Answer

oh, yeah!

wolf1728 · Answer

So you see x = 0.6881648129

kidthatbro8 · Answer

alright, thank you so much!!

wolf1728 · Answer

You are welcome.  I know taking logs of both sides seems pretty weird at first - but that's how you get the answer!