278^4x=37,800 find x

Question

lgbasallote · Answer

$$\huge 278^{4x} = 37,800$$
is that the question?

anonymous · Answer

yes

anonymous · Answer

anyone know?

anonymous · Answer

Take Log base 278 on both sides
so you get 4x = Log base 278 of 37800
Then on right hand side use change of base formula to change it to Ln 37800/Ln 278
so u get 4x =  Ln 37800/Ln 278
solve right side on calculator and divide that answer by 4 to get x

anonymous · Answer

i tried and i dont get the correct answer!

anonymous · Answer

i need the answer please

anonymous · Answer

$$b^x=A\iff x=\frac{\ln(A)}{\ln(b)}$$

anonymous · Answer

I am getting x = 0.47

anonymous · Answer

i got that too and its not correct thanks anyways though

anonymous · Answer

whats the correct answer ?

anonymous · Answer

i have no clue

anonymous · Answer

$$4x=\frac{\ln(37,800)}{\ln(278)}$$ $$x=\frac{4\ln(37,800)}{\ln(278)}$$ i get 7.49 http://www.wolframalpha.com/input/?i=4ln%2837800%29%2Fln%28278%29

anonymous · Answer

thanks guys
i have one more question if you have the time

anonymous · Answer

that should be correct 
my guess is there was a problem putting it in the calculator

anonymous · Answer

i think so

anonymous · Answer

@satellite73 why do you times it by 4

anonymous · Answer

you need parentheses, but since you are on a computer, type it in to wolfram as i did

anonymous · Answer

oh damn!

anonymous · Answer

because i made a mistake it is .468 http://www.wolframalpha.com/input/?i=ln%2837800%29%2F%284ln%28278%29%29

anonymous · Answer

thats what i got .468 rounded off to .47

anonymous · Answer

yes you are right
i am assuming that it was what not something like 
$$27\times 8^{4x}=37,800$$ right?

anonymous · Answer

yes thanks