Solve.
(1/4)^x+4 = √8
x+4 log 1/4= Log √8
I dont really no what to do from there...
$\displaystyle \left(\frac{1}{4}\right)^{x+4} = \sqrt{8}$
Note that
$\displaystyle \frac{1}{4} = 2^{-2}$
$\displaystyle \sqrt{8} = 2\sqrt{2} = 2^{1.5}$
Now you can convert all your numbers into base 2
$\displaystyle 2^{-2(x+4)} = 2^{1.5}$
Now if the bases are the same the exponents must also be the same
$\displaystyle -2x-8=1.5$
Solve the linear equation for x
I get x = -4.75
well what was previously shown is much better way to solve it
however if you need to solve with logarothms
$\displaystyle \left(x+4\right)\left(log1 - log4\right) = \frac{log8}{2}$
$\displaystyle
-xlog4 - 4log4 = \frac{log8}{2}
$
$\displaystyle
-xlog4 = \frac{log8 + 8log4}{2log4} = -4.75
$
have assumed some of the steps