Which of the following shows the true solution to the logarithmic equation solved below? log Subscript 2 Baseline (x) = log Subscript 2 Baseline (x 7) = 3. Log Subscript 2 Baseline left-bracket x (x 7) right-bracket = 3. X (x 7) = 2 cubed. X squared 7 x minus 8 = 0. (x 8) (x 1) = 0. X = negative 8, 1 x = negative 8 x = 1 x = 1 and x = negative 8 x = 1 and x = 8.

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shivishivangi1679 shivishivangi1679 · Answer 1 · 2022-04-18T13:20:47+02:00

The value which shows the true solution to the given logarithmic equation is 1.

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

The given logarithmic equation is,

[tex]\rm log_{2} (x) + log_{2} (x +7) = 3.[/tex]

Use the addition property of log in the above expression.

[tex]\rm log_{2} (x \times (x +7) )= 3.\\ (x \times (x +7) ) = 2^{3} \\x \times (x +7) = 8\\x^{2} +7x-8=0[/tex]

Solve the quadratic equation we get,

[tex](x+8)(x-1)=0[/tex]

x = -8, 1

Here, the logarithmic function is defined only for positive real numbers as its input.

Thus, the value which shows the true solution to the logarithmic equation solved above is 1.

Learn more about the domain and range of the function:

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