What does 4^2x-4=1 equal

Question

asked May 15, 2022 207k views

2 Answers

Karyon · Answer 1 · 2022-05-15T15:56:04+0000

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)