What are the x and y intercepts of the equation? y=log(12x+7)−3 Round the answers to the nearest hundredth.

ANSWER

The y-intercept is
[tex]y= - 2.15[/tex]


The x-intercept is
[tex]x= 82.75[/tex]


EXPLANATION


The given logarithmic equation is
[tex]y = log_{10}(12x + 7) - 3[/tex]



At x-intercept
[tex]y = 0[/tex]


This implies that,

[tex]0= log_{10}(12x + 7) - 3[/tex]

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

[tex]3= log_{10}(12x + 7) [/tex]

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

[tex] {10}^{3} = {10}^{log_{10}(12x + 7) } [/tex]



This implies that,

[tex]1000 = 12x + 7[/tex]



[tex]1000 - 7 = 12x[/tex]



This simplifies to,

[tex]993 = 12x[/tex]


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

[tex]x = \frac{993}{12} = 82.75[/tex]
correct to the nearest hundredth. Nearest hundredth means up to two decimal places.



For y-intercept,

[tex]x = 0[/tex]



This implies that,

[tex]y = log_{10}(12(0)+ 7) - 3[/tex]

This implies that,


[tex]y = log_{10}(0+ 7) - 3[/tex]


This simplifies to
[tex]y = 0.845 - 3[/tex]


This implies that,

[tex]y = - 2.15[/tex]
to the nearest hundredth.