we have 2 equations: 80 = ae^8b and 10 = ae^2b
how do i prove them to be b =(ln 8)/6???
this is what i have so far
ln 80 = ln ae^8b
ln 80 =8ba
what do i do with the a to get a 6??
how do i prove them to be b =(ln 8)/6???
this is what i have so far
ln 80 = ln ae^8b
ln 80 =8ba
what do i do with the a to get a 6??
-
80 = ae^(8b)
ln 80 = ln (ae^(8b)) = ln a + ln e^(8b) = ln a + 8b
10 = a e^(2b)
ln 10 = ln (ae^(2b)) = ln a + ln e^(2b) = ln a + 2b
subtract these two:
ln 80 - ln 10 = 8b - 2b
ln (80/10) = 6b
ln 8 = 6b ==> b = ln 8 / 6 QED
ln 80 = ln (ae^(8b)) = ln a + ln e^(8b) = ln a + 8b
10 = a e^(2b)
ln 10 = ln (ae^(2b)) = ln a + ln e^(2b) = ln a + 2b
subtract these two:
ln 80 - ln 10 = 8b - 2b
ln (80/10) = 6b
ln 8 = 6b ==> b = ln 8 / 6 QED