TITLE: How to find intersect of two continuous growth functions?
QUESTION [0 upvotes]: I am blanking on how to solve this type of equation. I have solved it using a graph, so I know the correct answer, but I need to solve it using log as well. EX: $1400e^{.046t}$ and $375e^{.352t}$.
Using a graph I got $t=4.304$, but I am unsure how to find their intersection using logarithmic functions. I think the multiplication instead of addition/subtraction is throwing me off
I started with:
$$1400(0.046t)\ln e=375(.352t)\ln e$$
$$1400(0.046t)=375(.352t)$$
I tried dividing both sides, subtracting, I know there is just one thing I am missing somewhere, but every thing I try I get different answers.
Thanks for your help!

REPLY [1 votes]: Your result is wrong because the correct rule for the logarithm of a product is
$$
\log(ab)=\log a+\log b
$$
so, from 
$$
1400e^{0.0467 t}=374e^{0.352 t}
$$
using the rule, we have
$$
\log\left(1400e^{0.0467 t}\right)=\log\left(374e^{0.352 t}\right) \iff \log 1400 +0.0467 t=\log 375 +0.352 t
$$
can you complete?
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