Question

Which equation can you solve to find the potential solutions to the equation log2x log2(x – 6) = 4? x2 – 6x – 4 = 0 x2 – 6x – 8 = 0 x2 – 6x – 16 = 0.

Answer 1

To solve the question we must know about Logarithm.

Logarithm

A log function is a way to find how much a number must be raised in order to get the desired number.

$a^c =b$

can be written as

$\rm{log_ab=c$

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.

$\rm{log_{10}1000=3$

The value of input can not be negative, the value of x is 8.

Given to us

• $\rm{ log_2x+log_2(x-6)= 4$

Solution

$\rm{ log_2x+log_2(x-6)= 4$

• Using $log_ab + log_ac = log_a(bc)$,

        $\rm{ log_2x(x-6)= 4$

• Taking antilog,

        $x(x-6)= 2^4$

• Doing factorization

        $x^2 -6x -16=0\\ x^2 -8x +2x-16=0\\ x(x-8)+2(x-8)=0\\ (x+2)(x-8) = 0$

Equating factors against 0,

1.    $(x+2)=0\\ x=-2$

2.     $(x-8)=0\\ x=8$

As the value of input can not be negative, the value of x is 8.

Hence, the value of x is 8.

Learn more about Logarithm:

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