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

Which of the following shows the extraneous solution

claudialopez093

10.03.2022

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:

log _ 7 ( 3 x ^ 3 + x ) - log _ 7 ( x ) = 2

We can rewrite it as:

$log7[\frac{3x^3+x}{x} ]=2$

But we know that log_7(49)=2

So, $log7[\frac{3x^3+x}{x} ]=log_7(49)$

Cancelling the log to get:

$\frac{3x^3+x}{x} =49$

Further simplifying it to get:

3x^2+1=49

3x^2=48

$x^2=\frac{48}{3}$

x^2=16

x = 4

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felicityhanson1252

14.05.2023

Both charge the same hourly rate, but a different fee.

Step-by-step explanation:

me 100

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