Question

2^(1-x)=3^x Can someone please help me solve this?

Answer 1

use log's

Answer 2

how do it do it? i know i have to use logs but i am completely lost as of how to start

Answer 3

2^(1-x) = 3^x

Multiply both sides by 2^(x-1):
1 = 2^(x-1) 3^x

1 = 2^(x-1) 3^x is equivalent to 2^(x-1) 3^x = 1:

2^(x-1) 3^x = 1

2^(x-1) 3^x = e^(log(2^(x-1))) e^(log(3^x))
= e^((x-1) log(2)) e^(x log(3))
= e^((x-1) log(2)+x log(3)):
e^(log(2) (x-1)+log(3) x) = 1

Take the natural logarithm of both sides:
ln(2) (x-1)+ln(3) x = 0

(log(2)+log(3)) x-log(2) = 0

=(log(2)+log(3)) x = log(2)

Answer 4

so x = ln2 / (ln2 + ln3)

Answer 5

Thank you so much!!! you explained it perfectly :)