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kudzordzifrancis
ANSWER

The solution is

[tex]x = 5[/tex]
EXPLANATION


We want to solve the logarithmic equation

[tex] log_{2}(3x - 7) = 3[/tex]
We take the antilogarithm of both sides to base 2.


In order words we need to rewrite the logarithmic equation as an exponential equation,

This implies that,


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


We evaluate the right hand side of the equation to obtain,


[tex]3x - 7 = 8[/tex]


We group the constant terms on the left hand side of the equation to obtain,


[tex]3x = 8 + 7[/tex]

This implies that

[tex]3x=15[/tex]

[tex]x = 5[/tex]
MrRoyal

The equation is a logarithm equation, and the solution to log₂(3x - 7) = 3 is x = 5

How to determine the solution?

The equation is given as:

log₂(3x - 7) = 3

Remove the logarithm symbol

3x - 7 = 2^3

Evaluate the exponent

3x - 7 = 8

Add 7 t both sides

3x = 15

Divide both sides by 3

x = 5

Hence, the solution to log₂(3x - 7) = 3 is x = 5

Read more about logarithms at:

https://brainly.com/question/13473114

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