The graph of y = log_{10x in the xy-plane intersects the y-axis at what value of y?

Rationale

It does not intersect the y-axis.

The graph of the function \( y = \log_{10}(x) \) is defined only for positive values of \( x \). Since the y-axis corresponds to \( x = 0 \), the logarithm is undefined at this point, meaning the graph does not intersect the y-axis.

A (0) YOUR ANSWER

The value of \( y \) equals 0 when \( x = 1 \) since \( \log_{10}(1) = 0 \). However, this does not pertain to an intersection with the y-axis, which occurs when \( x = 0 \), a value where the logarithm is undefined.

B (01-Oct) YOUR ANSWER

This option does not represent a numerical value relevant to the graph of the function. Regardless, the key point remains that the logarithm is undefined at \( x = 0 \), so there can be no intersection with the y-axis.

C (1) YOUR ANSWER

The value of \( y \) equals 1 when \( x = 10 \) because \( \log_{10}(10) = 1 \). This again does not indicate an intersection with the y-axis, where \( x = 0 \) renders the logarithm undefined.

D (10) YOUR ANSWER

The value of \( y \) equals 10 when \( x = 10^{10} \) since \( \log_{10}(10^{10}) = 10 \). Similar to previous options, this does not correspond to an intersection at \( x = 0 \).

Conclusion

The function \( y = \log_{10}(x) \) is only defined for \( x > 0 \), which excludes the y-axis where \( x = 0 \). Therefore, the graph does not intersect the y-axis at any value of \( y \), confirming that the correct answer is indeed that it does not intersect at all.

The graph of y = log_{10x in the xy-plane intersects the y-axis at what value of y?

It does not intersect the y-axis.

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