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(1 point)
Responses

x=5
x=5

x=11
x=11

x=19/5
x=19/5

x=13/11

Answer 1

8^x+1=16^2x-4

Answer 2

It seems like you are providing a list of equations or expressions for the variable \( x \). However, I need more context or a specific question related to these values to provide a more tailored response. Are you looking for solutions to an equation, simplification, or something else entirely? Please clarify!

Answer 3

To solve the equation \( 8^{x+1} = 16^{2x-4} \), we can start by expressing both sides in terms of base \( 2 \).

We know that:
- \( 8 = 2^3 \)
- \( 16 = 2^4 \)

So we can rewrite the equation as follows:

\[
(2^3)^{x+1} = (2^4)^{2x-4}
\]

Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we rewrite it:

\[
2^{3(x+1)} = 2^{4(2x-4)}
\]

Now we can simplify this:

\[
2^{3x + 3} = 2^{8x - 16}
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
3x + 3 = 8x - 16
\]

Now, rearranging the equation gives:

\[
3 + 16 = 8x - 3x
\]

This simplifies to:

\[
19 = 5x
\]

Now, we can solve for \( x \):

\[
x = \frac{19}{5}
\]

Thus, the solution to the equation \( 8^{x+1} = 16^{2x-4} \) is

\[
\boxed{\frac{19}{5}}.
\]