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il63 [147K]
3 years ago
6

Solve the logarithmic equation. y = log4 0.25 What does y equal?

Mathematics
1 answer:
Valentin [98]3 years ago
7 0

\bf \textit{exponential form of a logarithm} \\\\ log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies log_a b=y \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y=\log_4(0.25) ~\hfill 0.\underline{25}\implies \cfrac{025}{1\underline{00}}\implies \cfrac{1}{4}\implies 4^{-1} \\\\\\ y=\log_4\left( 4^{-1} \right)\implies 4^y=4^{-1}\implies y=-1

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<h3>Answer:</h3>

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<h3>Step-by-step explanation:</h3>

Functions describe the relationship between the dependent variable, y, and the independent variable, x.

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For a graph to be a function, x-values cannot repeat. This means that one x-value cannot have more than one y-value.

However, functions can have repeating y-values. So, y-values can have more than one x-value; as seen in quadratic functions. This means that answer B cannot be correct.

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The vertical line test is a way to determine if a graph is a function. A graph passes the vertical line test if you can draw a vertical line at every point on the coordinate plane and not have it intersect with the graph more than once.

On the graph in the question, a vertical line would intersect with the graph twice at the x-values greater than -1. Since the graph fails the vertical line test, it is not a function.

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