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tensa zangetsu [6.8K]
3 years ago
8

What does 4^2x-4=1 equal

Mathematics
2 answers:
slega [8]3 years ago
5 0

If the starting equation is

4²<em>ˣ</em> - 4 = 1

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

4²<em>ˣ</em> = 5

Take the base-4 logarithm of both sides:

log₄(4²<em>ˣ</em> ) = log₄(5)

Drop the exponent on the left, using the property \log_b(a^n)=n\log_b(a):

2<em>x</em> log₄(4) = log₄(5)

Now \log_b(b)=1 for any <em>b</em>, so

2<em>x</em> = log₄(5)

Solve for <em>x</em> by dividing both sides by 2:

<em>x</em> = 1/2 log₄(5)

You can also express this as

<em>x</em> = log₄(√5)

to make the solution slightly more compact.

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

<em>x</em> = log(5) / (2 log(4))

where the base of the logarithm is arbitrarily chosen. Then

<em>x</em> = log(5) / log(4²)

<em>x </em>= log(5) / log(16)

<em>x</em> = log₁₆(5)

Lisa [10]3 years ago
4 0

Answer:

x=2

Step-by-step explanation:

4^2x-4=4^0

2x-4=0

2x=4

x=4/2

x=2

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