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Examine the function [tex]f(x)=\log_3 x[/tex].

Which point is the intersection of [tex]f(x)[/tex] and the line [tex]y=1[/tex]?

A. [tex]\left(\frac{1}{3}, 1\right)[/tex]

B. [tex](3,1)[/tex]

C. [tex](1,3)[/tex]

D. [tex](1,1)[/tex]

Sagot :

GinnyAnsweridn
To find the intersection point between the function [tex]\( f(x) = \log_3(x) \)[/tex] and the line [tex]\( y = 1 \)[/tex], we need to determine the x-coordinate where the function [tex]\( f(x) \)[/tex] equals 1.

The function [tex]\( f(x) = \log_3(x) \)[/tex] represents the logarithm of [tex]\( x \)[/tex] with base 3. We are looking for the value of [tex]\( x \)[/tex] that makes this equation true:
[tex]\[ \log_3(x) = 1 \][/tex]

By definition of logarithms, [tex]\( \log_b(a) = c \)[/tex] means [tex]\( b^c = a \)[/tex]. Thus, we can rewrite the equation [tex]\( \log_3(x) = 1 \)[/tex] in exponential form:
[tex]\[ 3^1 = x \][/tex]

Solving this, we find:
[tex]\[ x = 3 \][/tex]

Therefore, the x-coordinate of the intersection point is [tex]\( x = 3 \)[/tex]. Since we are given that [tex]\( y = 1 \)[/tex] from the line equation [tex]\( y = 1 \)[/tex], the intersection point in the coordinate plane is:
[tex]\[ (3, 1) \][/tex]

So, the correct answer is [tex]\((3, 1)\)[/tex].
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