Question

What does 4^2x-4=1 equal

Answer 1

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
`\log_b(a^n)=n\log_b(a)`:

2x log₄(4) = log₄(5)

Now
`\log_b(b)=1` 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)

Answer 2

x=2

Explanation:

4^2x-4=4^0

2x-4=0

2x=4

x=4/2

x=2