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What is the solution of [tex]$\log _2(3 x-7)=3$[/tex]?

A. [tex]$\frac{1}{3}$[/tex]
B. 4
C. 5
D. [tex][tex]$\frac{16}{3}$[/tex][/tex]

Sagot :

GinnyAnswer
To solve the equation [tex]\(\log_2(3x - 7) = 3\)[/tex], let's follow these steps:

1. Understand the logarithmic equation: The given equation is in logarithmic form, which can be expressed as:
[tex]\[ \log_2(3x - 7) = 3 \][/tex]
This means that the expression [tex]\(3x - 7\)[/tex] is the power to which 2 must be raised to get the number 8.

2. Rewrite the logarithmic equation in exponential form: The equation [tex]\(\log_2(3x - 7) = 3\)[/tex] can be rewritten as:
[tex]\[ 3x - 7 = 2^3 \][/tex]
Here, [tex]\(2^3\)[/tex] represents 2 raised to the power of 3, which equals 8.

3. Simplify the exponential equation: Now, simplify the equation by substituting [tex]\(2^3\)[/tex] with 8:
[tex]\[ 3x - 7 = 8 \][/tex]

4. Solve for [tex]\(x\)[/tex]: To isolate [tex]\(x\)[/tex], first add 7 to both sides of the equation:
[tex]\[ 3x = 8 + 7 \][/tex]
This simplifies to:
[tex]\[ 3x = 15 \][/tex]

5. Divide by 3: Finally, divide both sides by 3 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{15}{3} \][/tex]
Simplifying the fraction gives:
[tex]\[ x = 5 \][/tex]

So, the solution to the equation [tex]\(\log_2(3x - 7) = 3\)[/tex] is [tex]\(x = 5\)[/tex].
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