Answered

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Solve for [tex]x[/tex].

[tex]2^{7x-3}=16[/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution is [tex]x = \square[/tex]
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

B. The solution is not a real number.

Sagot :

GinnyAnswer
To solve the equation [tex]\(2^{7x - 3} = 16\)[/tex], follow these steps:

1. Express 16 as a power of 2:
Notice that 16 can be written as a power of 2: [tex]\(16 = 2^4\)[/tex].

2. Rewrite the equation:
Since [tex]\(2^{7x - 3} = 16\)[/tex] and [tex]\(16 = 2^4\)[/tex], you can equate the exponents of 2. This gives:
[tex]\[ 7x - 3 = 4 \][/tex]

3. Solve for [tex]\(x\)[/tex]:
- Add 3 to both sides of the equation:
[tex]\[ 7x - 3 + 3 = 4 + 3 \][/tex]
Simplifying this, you get:
[tex]\[ 7x = 7 \][/tex]

- Divide both sides by 7:
[tex]\[ x = \frac{7}{7} \][/tex]
Simplifying this, you get:
[tex]\[ x = 1 \][/tex]

So, the solution is [tex]\(x = 1\)[/tex].

Answer:
A. The solution is [tex]\(x = 1\)[/tex]
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