Verified Answer :

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 \(\log _2 (3x-7) = 3\)

Explanation:

Given that: \(\log _2 (3x-7) = 3\)

Using logarithmic properties:

if \(\log_a x = b\)

then;

\(x = b^a\)

Apply this rule on the given equation:

\((3x-7) = 2^3\)

⇒\(3x-7= 8\)

Add 7 to both sides we get;

\(3x= 15\)

Divide both sides  by 3 we get;

x = 5

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