4^2b=1/16

Solution for 4^2b=1/16 equation:

4^2b=1/16

We move all terms to the left:

4^2b-(1/16)=0

We add all the numbers together, and all the variables

4^2b-(+1/16)=0

We get rid of parentheses

4^2b-1/16=0

We multiply all the terms by the denominator


4^2b*16-1=0

Wy multiply elements

64b^2-1=0

a = 64; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·64·(-1)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*64}=\frac{-16}{128}
=-1/8
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*64}=\frac{16}{128}
=1/8
$