Question

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.

Answer 1

Answer: Plot of
`\log y` vs
`x` would be linear with a slope of 4.

Step-by-step explanation:

Given

Equation is
`y=10^(4x)`

Taking log both sides

`\Rightarrow \log y=4x\log (10)\\\Rightarrow \log y=4x`

It resembles with linear equation
`y=mx+c`

Here, slope of
`\log y` vs
`x` is 4.