Question 80047
1/32=2^1-x
:
If you remember the powers of 2, you can look at this: 2^-5 = 1/32
Therefore x = 6; however they may want you to use logs to solve it
:
{{{2^(1-x)}}} = {{{1/32}}}
:
{{{ln(2^(1-x))}}} = {{{ln(1/32)}}}; nat log of both sides
:
(1-x)*ln(2) = {{{ln(1/32)}}}; log equiv of exponents
:
.693147(1-x) = -3.4657
:
.69347 - .69347x = -3.4657
:
-.69347x = -3.4657 - .69347
:
-.69347x = -4.1592
:
x = -4.1592/-.69347
:
x = +5.9976 ~ 6
:
:
Check: 2^(1-6) = 2^-5 = 1/2^5 which is 1/32