Since I'm working databases that are subject to change, I would like to be
able to make my own trendline formulas. The built-in trendline function of
excel doesn't let me use the trendline formula shown in the graph, and I
don't want to manually change my formulas each time my database changes.

I've been able to make my own linear- and 'power'trendlines as follows:

My linear trendline:
form: y=a*x+b
a=SLOPE(Yrange;Xrange)
b=INTERCEPT(Yrange;Xrange)

Mijn 'Power'trendline:
form: y=a*x^b
a=EXP(INTERCEPT(LN(Yrange);LN(Xrange)))
b=SLOPE(LN(Yrange);LN(Xrange))

So currently I'm looking for the following two:
Logarithmic trendline in the form:
y=a*Ln(x)+b
Exponential trendline in the form:
y=a*e^(b*x)

Thanks in advance,

Maarten