(130)[(0.07)^n] = (100)[(0.08637)^n]. How to find the n value by putting ln?
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A simple starting step which is not essential is to divide both sides by 100:
1.3[(0.07)^n] = (0.08637)^n
Now take natural log of both sides, using the properties
ln(xy) = lnx + lny
and ln(x^p) = p lnx
this gives
ln(1.3) + n ln(0.07) = n ln(0.08637)
Hence ln(1.3) = n[ln(0.08637) - ln(0.07)]
and so
n = ln(1.3) / (ln(0.08637) - ln(0.07))
.. = 1.248490688
EDIT: Another non-essential step at the start would be to divide by 0.07^n, giving
1.3 = (0.08637/0.07)^n = 1.234^n (near enough; actually (1.233857142857142857142...)^n)
then take ln of both sides.
1.3[(0.07)^n] = (0.08637)^n
Now take natural log of both sides, using the properties
ln(xy) = lnx + lny
and ln(x^p) = p lnx
this gives
ln(1.3) + n ln(0.07) = n ln(0.08637)
Hence ln(1.3) = n[ln(0.08637) - ln(0.07)]
and so
n = ln(1.3) / (ln(0.08637) - ln(0.07))
.. = 1.248490688
EDIT: Another non-essential step at the start would be to divide by 0.07^n, giving
1.3 = (0.08637/0.07)^n = 1.234^n (near enough; actually (1.233857142857142857142...)^n)
then take ln of both sides.