`0.5^x-0.25=4` Solve the equation.

Expert Answers

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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`


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)` .



To isolate the x, divide both sides by `ln(0.5)` .




`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` .







`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` .

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