anonymous 4 years ago Ex cause me, how can I solve this equations ? 3^(x-1)= 5^(x-2)

1. anonymous

did you see your previous post? Are you going to solve by graphing?

2. anonymous

start with $(x-1)\ln(3)=(x-2)\ln(5)$ and then do a raft of algebra

3. anonymous

$\ln(3)x-\ln(3)=\ln(5)x-2\ln(5)$ $ln(3)x-\ln(5)x=\ln(3)-2\ln(5)$ $(\ln(3)-\ln(5))x=\ln(3)-2\ln(5)$ $x=\frac{\ln(3)-2\ln(5)}{\ln(3)-\ln(5)}$

4. anonymous

check my algebra because is is early and i could have made a mistake. also don't fret if this is not the answer in the back of the book because there are many ways to write this using the properties of the log

5. anonymous

thank you.

6. anonymous

you will also notice that this is an answer only a math teacher could love, because it doesn't really tell you what the number is at all, just writes in terms of logs. if you want an actual decimal approximation, do what meverette suggested and graph

7. anonymous

yw