Which of the following shows the extraneous solution to the logarithmic equation log Subscript 7 Baseline (3 x cubed + x) minus

Question

Gala2k [10]

2 years ago

4

Which of the following shows the extraneous solution to the logarithmic equation log Subscript 7 Baseline (3 x cubed + x) minus

log Subscript 7 Baseline (x) = 2 x = negative 16 x = negative 4 x = 4 x = 16

Mathematics

2 answers:

xeze [42] · Answer 1 · 2023-03-25T13:45:58+03:00

xeze [42]2 years ago

7 0

Answer:

x = - 4

Step-by-step explanation:

Got it right :)

tresset_1 [31] · Answer 2 · 2023-03-25T11:58:49+03:00

Answer:

x = -4

Step-by-step explanation:

A graphing calculator shows there is one solution to ...

$\log_7{(3x^2+x)}-\log_7{(x)}=2$

However, the usual solution method would be to combine the logarithms and take the antilog to get ...

$\log_7{\left(\dfrac{3x^3+x}{x}\right)}=2\\\\\log_7{(3x^2 +1)}=2\\\\3x^2+1=7^2\\\\x^2=\dfrac{49-1}{3}=16\\\\x=\pm 4\qquad\text{take the square root}$

This gives two solutions. the "solution" x = -4 is extraneous, as it doesn't work in the original equation. "x" must be positive in the log expressions.