normacruz1554
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Which point corresponds to the real zero of the graph of [tex][tex]$y=\log _3(x+2)-1$[/tex][/tex]?

A. [tex][tex]$(-1,-1)$[/tex][/tex]
B. [tex][tex]$(1,0)$[/tex][/tex]
C. [tex][tex]$(-1.0)$[/tex][/tex]
D. [tex][tex]$(0,-369)$[/tex][/tex]

Sagot :

GinnyAnswer
To determine which point corresponds to the real zero of the graph of [tex]\( y = \log_3(x + 2) - 1 \)[/tex], we need to find the value of [tex]\( x \)[/tex] that makes [tex]\( y = 0 \)[/tex].

Given the equation:

[tex]\[ y = \log_3(x + 2) - 1 \][/tex]

Set [tex]\( y \)[/tex] to 0, since we are looking for the real zero:

[tex]\[ 0 = \log_3(x + 2) - 1 \][/tex]

Now, solve for [tex]\( x \)[/tex]:

First, isolate the logarithmic term:

[tex]\[ \log_3(x + 2) = 1 \][/tex]

To remove the logarithm, recall the definition of a logarithm: if [tex]\(\log_b(a) = c\)[/tex], then [tex]\(b^c = a\)[/tex]. Here, our base is 3, and our logarithm equals 1:

[tex]\[ 3^1 = x + 2 \][/tex]

Evaluate the exponent:

[tex]\[ 3 = x + 2 \][/tex]

Now, solve for [tex]\( x \)[/tex]:

[tex]\[ x = 3 - 2 \][/tex]

[tex]\[ x = 1 \][/tex]

So, the real zero of the function occurs at [tex]\( x = 1 \)[/tex]. This gives us the point:

[tex]\[ (1, 0) \][/tex]

Therefore, the point which corresponds to the real zero of the graph of [tex]\( y = \log_3(x + 2) - 1 \)[/tex] is [tex]\((1, 0)\)[/tex].

The correct answer is: [tex]\((1, 0)\)[/tex].
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