Posted by **Peter** on Friday, January 20, 2012 at 1:54am.

solve 3^x=4^(x-2)

- Maths -
**Reiny**, Friday, January 20, 2012 at 9:59am
take ln of both sides

ln (3^x) = ln (4^(x-2))

x(ln3) = (x-2)(ln4)

= x(ln4) - 2ln4

xln3 - xln4 = -2ln4

x(ln3 - ln4) = -2ln4

x = -2ln4/(ln3-ln4)

or

x = 2ln4/(ln4 - ln3)

if get appr. 9.638

check:

3^9.638 = appr. 39672.63

4^7.638 = 39676.6

----- close enough using only 3 decimals, if I use my calculator's memory and store the full value of x, my error is 5.9x10^-6

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