Question

What are the x and y intercepts of the equation?

y=log(12x+7)−3

Round the answers to the nearest hundredth.

Answer 1

ANSWER

The y-intercept is

`y= - 2.15`


The x-intercept is

`x= 82.75`


Step-by-step explanation


The given logarithmic equation is

`y = log_(10)(12x + 7) - 3`



At x-intercept

`y = 0`


This implies that,


`0= log_(10)(12x + 7) - 3`

We add 3 to both sides of the equation to obtain,


`3= log_(10)(12x + 7)`

We now take the antilogarithm of both sides to base 10 to obtain,


`{10}^(3) = {10}^{log_(10)(12x + 7) }`



This implies that,


`1000 = 12x + 7`




`1000 - 7 = 12x`



This simplifies to,


`993 = 12x`


We divide both sides of the equation by 12 to obtain,


`x = (993)/(12) = 82.75`
correct to the nearest hundredth. Nearest hundredth means up to two decimal places.



For y-intercept,


`x = 0`



This implies that,


`y = log_(10)(12(0)+ 7) - 3`

This implies that,



`y = log_(10)(0+ 7) - 3`


This simplifies to

`y = 0.845 - 3`


This implies that,


`y = - 2.15`
to the nearest hundredth.