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!
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Responses
x=5
x=5
x=11
x=11
x=19/5
x=19/5
x=13/11
3 answers
8^x+1=16^2x-4
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
\[ \boxed{\frac{19}{5}}. \]