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2 years ago

8. While solving the equation log,(8x) – log,(x2 - 1) = log, 3, Karla found possible solutions at x=3

Mathematics

1 answer:

TiliK225 [7]2 years ago

3 0

The possible solution to the equation given is 3 and -1/3

<h3>Laws of logarithm</h3>

Given the logarithmic expression given as:

log,(8x) – log,(x^2 - 1) = log, 3

Applying the product and quotient rule will give:

log(8x/x^2-1) = log3

8x/x^2-1 = 3

Cross multiply

8x = 3x^2 - 3

3x^2 - 8x - 3 = 0

3x^2 -9x + x - 3 = 0

3x(x-3)+1(x-3)

x - 3 = 0 and 3x = -1

x = 3 and -1/3

Hence the possible solution to the equation given is 3 and -1/3

Learn more on logarithm here: brainly.com/question/25710806

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$x_{3} = 2.28153641 - \frac{2.28153641 -3\sin(2.28153641)}{1 -3\cos(2.28153641)} = 2.2788654$

$x_{4} = 2.2788654 - \frac{2.2788654 -3\sin(2.2788654)}{1 -3\cos(2.2788654)} = 2.2788627$

$x_{5} = 2.2788627 - \frac{2.2788627-3\sin(2.2788627)}{1 -3\cos(2.2788627)} = 2.2788627$

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$x \approx 2.278863$

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