Question

Can someone explain how to get the answer to this problem? Preferably step by step please!

If 5^{-x+3}=2, then 5^{x-2}= ?

Thank you!! :)

Answer 1

you want to find a value of x that makes it seem plausible but only when you take a quick glance :)

Answer 2

(-x+3) ln(5) = ln(2)

-x+3 = ln(2)/ln(5)

-x = (ln(2)/ln(5)) - 3

x = -(ln(2)/ln(5)) + 3

insert that value into the other side to solve

Answer 3

I used log instead of ln, it's the same thing right?

Answer 4

yeah, i used ln casue its quicker to type than log and not as much room for error ;)

Answer 5

you coulda used log5 as well, but then log5(2) seems superfluous

Answer 6

For some reason, I'm getting weird answers instead of the choices given. The choices are 10, 25, 5/2 and 2/5.

Answer 7

for x or for the new value?

Answer 8

I typed the question exactly the way it's stated. I'm guessing it's after the value?

Answer 9

5^(-(ln(2)/ln(5)) + 3 - 2)

5^(-(ln(2)/ln(5)) + 1) = 2.5

http://www.wolframalpha.com/input/?i=5^%28-%28ln%282%29%2Fln%285%29%29+%2B+1%29

Answer 10

2.5 = 2' 1/2 = 5/2

Answer 11

Wow! Thank you!

Answer 12

yw :)