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