I'm needing help with solving two equations using logarithms:
I know by "plugging and chugging" into x, the it's somewhere around 48. However, I'd like to know how to solve it the real way. Here's what I'm trying:
Take the log of both sides log 15000 = log 702.712 (1.067) ^ x
Drag the x out front 4.176 = (x) log 702.712 (1.067)
But when I try to solve it any further, I get x equaling around 1 or 2... not right at all.
Am I solving this equation wrong?
Also, there is one more involving Pe^rt (continuous growth formula)
2) 60000 = 10000e^.062t
Because this equation involves e, I take the natural log of both sides:
ln 60000 = ln 10000 e ^ .062 t
I drag .062t out front:
ln 60000 = (.062t) ln 10000
I divide by ln 10000:
1.1945 = .062 t
Divide by .062,
19.266 = t
That's all good, I managed to solve the entire equation, except the teacher specifically told us our answer should come out between t= 25 and t=30. I think the answer should be around t=29
So, I have two equations here. I know what the answer SHOULD be, but it really frustrates me that I can't solve them and come up with the answer myself. Can you guys point out where I might be going wrong?