Revised: Can you solve 2Eq = 1Eq * (1 + ROE)^x

Question

 

I would like to solve for x in the following formula:

2Eq = 1Eq * (1 + ROE)^x

Eq = Equity and is a known value

ROE = Return on equity and is a known value

x is the unknown value

I would like to set up the formula so that x is isolated on one side of the equation and I can plug in the known values to determine the value of x.

Thanks!

Answer 1

2eq=eq*(1+roe)^x

2eq/eq =(1+roe)^x

2=(1+roe)^x

log(2)=log[(1+roe)^x]

log(2)+x*log(1+roe)

x=log(2)/log(1+roe)

log10(2)=0.301029995

giv me a roe & kan du log onit

Answer 2

Thank you for your help.  It works.  In Excel speak, I was able to validate it using:

X = LN(2)/LN(1+ROE)

I finally realized the formula is effectively the rule of 72 ... the number of year to double at a given rate of return.