0.5^x-0.25=4 Solve the equation.

For the given equation 0.5^x-0.25=4 , we may simplify by combining like terms.
Add 0.25 on both sides of the equation.
0.5^x-0.25+0. 25=4+0.25
0.5^x=4.25
Take the "ln " on both sides to be able to bring down the exponent value.
Apply the natural logarithm property: ln(x^n)= n*ln(x) .
ln(0.5^x)=ln(4.25)
xln(0.5)=ln(4.25)
To isolate the x, divide both sides by ln(0.5) .
(xln(0.5))/(ln(0.5))=(ln(4.25))/(ln(0.5))
x=(ln(4.25))/(ln(0.5))
x=(ln(17/4))/(ln(1/2))
x=(ln(17) -ln(4))/(ln(2^(-1)))
x=(ln(17) -ln(2^2))/(ln(2^(-1)))
x=(ln(17) -2ln(2))/(-ln(2))
x=(ln(17))/(-ln(2)) -(2ln(2))/(-ln(2))
x= -(ln(17))/(ln(2)) +2 or -2.087 (approximated value)
Checking: Plug-in x=-2.087 on 0.5^x-0.25=4 .
0.5^(-2.087)-0.25=?4
(1/2)^(-2.087)-0.25=?4
(2^(-1))^(-2.087)-0.25=?4
2^((-1)*(-2.087))-0.25=?4
2^(2.087)-0.25=?4
4.25-0.25=?4
4=4   TRUE
Note: 2^(2.087)=4.248636746 ~~4.25
Therefore,there is no extraneous solution.
The x=-(ln(17))/(ln(2)) +2   is the real exact solution of the given equation 0.5^x-0.25=4 .