Question

Someone help please i dont know how to work this problem..

Solve. Round your answer to three decimal places.

5^x+1=4^x-1

Answer 1

i am going to assume that this is
\[5^{x+1}=4^{x-1}\]

Answer 2

satellite always gives the best answers

Answer 3

@satellite73 yes

Answer 4

start with
\[(x+1)\ln(5)=(x-1)\ln(4)\] and then do a raft of algebra
is the first step clear?

Answer 5

yes

Answer 6

ok then it is algebra from here on in
don't forget that while \(\ln(x)\) is a function, \(\ln(5)\) is a number, some constant

Answer 7

-13.425 :)

Answer 8

so we start with
\[(x+1)\ln(5)=(x-1)\ln(4)\] multiply out to get
\[\ln(5)x+\ln(5)=\ln(4)x-\ln(4)\] then put the x's on one side via
\[\ln(5)x-\ln(4)x=-\ln(4)-\ln(5)\] factor out the x to get
\[(\ln(5)-\ln(4))x=-\ln(4)-\ln(5)\] then divide to get
\[x=\frac{-\ln(4)-\ln(5)}{\ln(5)+\ln(4)}\]