Question

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What are the x and y intercepts of the equation?

y=log(7x+3)−2



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Answer 1

$Domain:\\7x+3>0\qquad\text{subtract 3 from both sides}\\7x>-3\qquad\text{divide both sides by 7}\\x>-\dfrac{3}{7}$

$x-intercept\ for\ y=0:\\\\\log(7x+3)-2=0\qquad\text{add 2 to both sides}\\\\\log(7x+3)=2\\\\\log(7x+3)=\log10^2\iff7x+3=100\qquad\text{subtract 3 from both sides}\\\\7x=97\qquad\text{divide both sides by 7}\\\\x\approx13.86\\\\y-intercept\ for\ x=0:\\\\y=\log(7(0)+3)-2\\\\y=\log(3)-2\approx-1.52\\\\Answer:\\x-intercept=\boxed{13.86}\\y-intercept=\boxed{-1.52}$

Answer 2

The required x = 13.86 and y = -1.52 are the intercept of the equation.

Given that,

Equation; y = log(7x+3) -2,

We have to find,

What are the x and y-intercept of the equation?

According to the question,

To find the intercept of the given equation the term 7x+3>0 and finding domain, following all the steps given below.

$7x + 3>0 \\\\7x >-3 \\\\x > \dfrac{-3}{7}$

Then,

For the x-intercept, becomes y = 0,

$log (7x+3) - 2= 0\\\\log (7x+3) = 2$

Taking log base 10 both the sides,

$log(7x+3) = log10^2\\\\7x + 3 = 100\\\\7x = 100-3\\\\7x = 97\\\\x = \dfrac{97}{7}\\\\x = 13.86$

And for y-intercept becomes x = 0,

$y = log (7(0)+3) - 2\\\\y = log 3 - 2\\\\y = 0.48 - 2\\\\y = -1.52$

Hence, The required x = 13.86 and y = -1.52 are the intercept of the equation.

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