Question

Y=log(12x+7)-3

What are the x and y intercepts of the equation rounded to the nearest hundredth?

Answer 1

x-intercept = 82.75,

y-intercept = -2.15

Explanation:

Since, intercepts of a function are the value of x and y at which the graph of the function intercept the coordinate axis.

Given function,

`y = \log (12x + 7) - 3`

For x-intercept,

y = 0,

`\implies 0 = \log (12x + 7) - 3`

`3 = \log (12x + 7)`

`10^3 =12x + 7`
`(n = \log_m a \implies m^n =a)`

`1000 - 7 = 12x`

`993 = 12x`

`\implies x = (993)/(12)=82.75`

For y-intercept,

x = 0,

`y = \log (12(0) + 7) - 3= \log 7 - 3\approx -2.15`

Answer 2

x -intercepts (nearest to hundredths) = 82.75

y -intercepts (nearest to hundredths) = -2.15

Explanation:

Given the function: y= log (12x+7) - 3 ......[1]

x-intercepts states that the graph crosses the x-axis or

In other words x-intercepts is the point on the graph where y= 0.

Now, substitute the values of y = 0 in [1] to solve for x;

0 = log(12x + 7) - 3

Add both sides 3 we get;

0 + 3 = log(12x + 7) - 3+ 3

Simplify:

3 = log (12x+7)

Using :
`log a= b` ⇒
`a = 10^b`

Then;

12x + 7 =
`10^3`

or

12x + 7 = 1000

Subtract 7 to both sides of an equation we have;

12x + 7 - 7= 1000 - 7

Simplify:

12x = 993

Divide both sides by 12 we get;

x = 82.75

Therefore, x - intercept = 82.75

Y-intercepts states that the graph crosses the y-axis or

In other words y-intercepts is the point on the graph where x= 0

Substitute the value of x =0 in [1] to solve for y;

y = log(12(0) +7) -3

y = log(7) -3

y = 0.84509804- 3 = - 2.15490196

therefore, y -intercepts (nearest to hundredths) is, -2.15