how can i solve exponential equation 50^x = 17

Question

anonymous · Answer

you stupid boy

anonymous · Answer

flutter off..

anonymous · Answer

i need to make the bases equal..

hitaro9 · Answer

So, you're looking to find 50 to what power = 17. 

Knowing that 17 is less than 50, you can assume that x is going to be less than 1. Now. have you learned about logarithms yet?

anonymous · Answer

Kind of, its going to be a fraction isnt it

hitaro9 · Answer

You know it's going to be less than 1, so yeah.

anonymous · Answer

how would solving this be different with equal bases?

hitaro9 · Answer

Okay, so 17 = 50^x

can be changed to 

$$\log_{50}(17)$$ = x

anonymous · Answer

oh i forgot about this!

anonymous · Answer

so now i solve for x?

hitaro9 · Answer

You need a numeric answer? log50(17) won't do?

anonymous · Answer

the question is asking: Erika was working on solving the exponential equation 50x = 17; however, she is not quite sure where to start. Using complete sentences, describe to Erika how to solve this equation and how solving would be different if the bases were equal.

hitaro9 · Answer

I mean, I just used the basic definition of logarithms to find the answer. 

logb(y)=x is the same as b^x = y

hitaro9 · Answer

beyond that I don't really remember how one goes about finding logs.

hitaro9 · Answer

You could say she could just guess and check, but I doubt your teacher wants that.

anonymous · Answer

i just need to know what the equal base is, i havent sound one yet.

anonymous · Answer

found

hitaro9 · Answer

If the bases are equal then the problem is really easy

If 50^x = 50^2 then x=2

You simply set the exponents equal to one another.

anonymous · Answer

that does not make any sense to me.. 50^2 is not equal to 17...

hitaro9 · Answer

Well I think it's just a what if kind of thing, unless I'm misunderstanding what they're asking?

hitaro9 · Answer

"describe to Erika how to solve this equation and how solving would be different if the bases were equal."

if the bases were equal

The bases aren't equal so it's not really relevant to the problem.

anonymous · Answer

it would look something like this.. (x)^(x)(n)=(x)^(n) i think

hitaro9 · Answer

I'm sorry, I just don't know what the problem is asking. Maybe someone else can help ya'

anonymous · Answer

ok thanks i think i figured it out 50^x=50^(.34)

hitaro9 · Answer

Alright.