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vodka [1.7K]
3 years ago
12

Which of the following is true regarding the solutions to the logarithmic equation below? 2 log Subscript 6 Baseline (x) = 2. lo

g Subscript 6 Baseline (x squared) = 2. x squared = 6 squared. x squared = 36. x = 6, negative 6. x = 6 and x = negative 6 are true solutions x = 6 and x = negative 6 are extraneous solutions x = 6 is a true solution and x = negative 6 is an extraneous solution x = 6 is an extraneous solution and x = negative 6 is a true solution
Mathematics
2 answers:
Serggg [28]3 years ago
4 0

Option c: x=6 is a true solution and x=-6 is an extraneous solution.

Explanation:

The equation is 2 \log _{6} x=2

Dividing both sides of the equation by 2, we get,

\frac{2 \log _{6}(x)}{2}=\frac{2}{2}

Simplifying,

\log _{6}(x)=1

Since, we know by the logarithmic definition, if \log _{a}(b)=c, then b=a^{c}

Using this definition, we have,

x=6^{1}

Hence, x=6

Now, let us verify if x=6 is the solution.

Substitute x=6 in the equation 2 \log _{6} x=2 to see whether both sides of the equation are true.

We have,

2 \log _{6}(6)

Using the log rule, \log _{a}(a)=1

We have,

2*1=2

Hence, both sides of the equation are equal.

Thus, x=6 is the true solution.

Lapatulllka [165]3 years ago
3 0

Answer:

C is the answer i got it correct

Step-by-step explanation:

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