"How do you solve 8x=4?" was answered by students like you

Irvin Dukes Answered2021-12-23

How do you solve

8^{x} = 4

Answer & Explanation

Jack Maxson

Expert

2021-12-24Added 25 answers

8^{x} = 4 \Leftrightarrow x = \frac{2}{3}

Explanation:

8^{x} = 4

Since

4 = (2) (2) = 2^{2}

we can say that

8 = 4 (2) = (2) (2) (2) = 2 (2^{2}) = 2^{2 + 1} = 2^{3}

So by changing notation we get

\Leftrightarrow {(2^{3})}^{x} = 2^{2}

and since

{(x^{a})}^{b} = x^{a b}

, we can say

\Leftrightarrow 2^{3 x} = 2^{2}

Then we take the

\ln_{2} (x)

of both sides

\Leftrightarrow \ln_{2} (2^{3 x}) = \ln_{2} (2^{2})

This gives us

\Leftrightarrow 3 x = 2

Then we divide both sides by 3 to isolate x

\Leftrightarrow x = \frac{2}{3}

and we have our answer

ramirezhereva

Expert

2021-12-25Added 28 answers

Solve for x over the real numbers:

8^{x} = 4

Hint:
Eliminate the exponential from the left hand side.
Take the logarithm base 8 of both sides:
Answer:

x = \frac{2}{3}

user_27qwe

Expert

2021-12-30Added 230 answers

First answer is more helpful

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