Respuesta :

mpanderla95
To solve this question, all you have to do is take 2 raise it to 3, and make it equal to the expression 3x-7 and solve for x.
2^3=3x-7
8=3x-7
8+7=3x
15=3x
15/3=3x/3
5=x.
X=5.
You can verify if the answer is correct by plugging the value of 5 back into the original logarithmic equation.

Answer:

x = 5 is the solution of [tex]\log _2 (3x-7) = 3[/tex]

Explanation:

Given that: [tex]\log _2 (3x-7) = 3[/tex]

Using logarithmic properties:

if [tex]\log_a x = b[/tex]

then;

[tex]x = b^a[/tex]

Apply this rule on the given equation:

[tex](3x-7) = 2^3[/tex]

⇒[tex]3x-7= 8[/tex]

Add 7 to both sides we get;

[tex]3x= 15[/tex]

Divide both sides  by 3 we get;

x = 5

therefore,  the solution of [tex]\log _2 (3x-7) = 3[/tex] is 5

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