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mathmate

If the question is

[tex]log_2(x)+log_2(x-6)=4[/tex]

which can be simplified to

[tex]log_2(x(x-6))=4[/tex]

By the definition of log, [tex]log_a(x)=y[/tex] means [tex]a^y=x[/tex]

=>

2^4=x(x-6)=x^2-6x

Simplify and solve for x

x^2-6x-16=0

(x+2)(x-8)=0

x=-2 or x=8

Since no answer choices are given, one of the equations in the above solution should appear in the answer choices.

abidemiokin

The value of x from the given logarithmic expression are -2 and 8

Indices and law of Indices

Given the expression

log2x + log2(x – 6) = 4

Applying the product rule in indices

log2(x(x-6)) = 4

log2(x²-6x) = log2 16

Cancelling log on both sides, we will have;

x² - 6x = 16

Equate to zero

x² - 6x - 16 = 0

x² -8x +2 x - 16 = 0

x(x-8) + 2(x-8) = 0

x = -2 and 8

Hence the value of x from the given logarithmic expression are -2 and 8

Learn more on logarithm here: https://brainly.com/question/13473114

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