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Consider the equation y = 10^(4x). Which of the following statements is true?


A plot of log(y) vs. x would be linear with a slope of 4.


A plot of log(y) vs. log (x) would be linear with a slope of 10.


A plot of log(y) vs. x would be linear with a slope of 10.


A plot of y vs. log(x) would be linear with a slope of 4.


A plot of log(y) vs. log (x) would be linear with a slope of 4.


A plot of y vs. log(x) would be linear with a slope of 10.

Respuesta :

Answer: Plot of  [tex]\log y[/tex] vs [tex]x[/tex] would be linear with a slope  of 4.

Explanation:

Given

Equation is [tex]y=10^{4x}[/tex]

Taking log both sides

[tex]\Rightarrow \log y=4x\log (10)\\\Rightarrow \log y=4x[/tex]

It resembles with linear equation [tex]y=mx+c[/tex]

Here, slope of [tex]\log y[/tex] vs [tex]x[/tex] is 4.