I am having difficulty with setting two exponential growth equations equal to one another to find where they catch up (intersect) with each other. I have this so far:

(1.03) ^ t/5 = .4 (1.08) ^ t/3 .

My professor gave me a hint of ln(ab) = ln(a) + ln(b), but I'm not sure where to go with that.

Any help would be greatly appreciated!

when you put "ln" onto a number, the exponent "comes down in front"

(t/5)*ln (1.03) = ln (.4*(1.08^(t/3)))

then, using the professor's hint

(t/5)*ln (1.03) = ln (0.4) + (t/3)*ln(1.08)

and take it from there.

Thank you so much! That helped a lot. :)