What does 4^2x-4=1 equal

If the starting equation is

4²ˣ - 4 = 1

first move the 4 on the left to the right side:

4²ˣ = 5

Take the base-4 logarithm of both sides:

log₄(4²ˣ ) = log₄(5)

Drop the exponent on the left, using the property :

2x log₄(4) = log₄(5)

Now for any b, so

2x = log₄(5)

Solve for x by dividing both sides by 2:

x = 1/2 log₄(5)

You can also express this as

x = log₄(√5)

to make the solution slightly more compact.

You can also use the change-of-base identity to rewrite the solution as

x = log(5) / (2 log(4))

where the base of the logarithm is arbitrarily chosen. Then

x = log(5) / log(4²)

x = log(5) / log(16)

x = log₁₆(5)

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!