Which of the following shows the extraneous solution to the logarithmic equation x = -16 x = -4 x = 4 x = 16

The correct answer option is x = 4.

Step-by-step explanation:

We are given the following logarithmic equation and we are to determine whether which of the given options shows its extraneous solution:

We can rewrite it as:

But we know that

So,

Cancelling the log to get:

Further simplifying it to get:

x = 4

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

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