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Question

Question
Tariq wants to solve for x in the equation 8^x+1=16^2x-4

Select All

(1 point)
Responses

x=5
x=5

x=11
x=11

x=19/5
x=19/5

x=13/11

Answer 1

To solve the equation \( 8^{x+1} = 16^{2x-4} \), we can start by rewriting both sides with a common base.

The numbers 8 and 16 can be expressed as powers of 2:

• \( 8 = 2^3 \)
• \( 16 = 2^4 \)

Now we can rewrite the equation:

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

This simplifies to:

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

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

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

Expanding both sides:

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

Now, let's get all x terms on one side and constant terms on the other side:

\[ 3 + 16 = 8x - 3x \] \[ 19 = 5x \]

Now, solve for \( x \):

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

So, the solution to the equation is \( x = \frac{19}{5} \).

Among the provided options, the only correct solution is \( x = \frac{19}{5} \).

The final answer is:

• x = 19/5

Answer 2

Select all that apply

Answer 3

Given the options you provided and the solution we obtained, let's analyze each one:

1. \( x = 5 \) - Not correct
2. \( x = 11 \) - Not correct
3. \( x = \frac{19}{5} \) - Correct
4. \( x = \frac{13}{11} \) - Not correct

Thus, the only option that applies is:

• x = 19/5

So, the answer to "Select all that apply" is:

• x = 19/5