Strawberrykid2004idn
Answered

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What function is the inverse of the exponential function y = 3^x?

Sagot :

GeorgePPidn

Answer:

Step-by-step explanation:

First switch the y and x values:

[tex]x=3^y[/tex]

Take the natural log of both sides to get:

[tex]\ln(x)=y*\ln(3)[/tex]

Separate the y value:

[tex]y=\frac{\ln(x)}{\ln(3)}[/tex]

Cricetusidn

The inverse of the exponential function will be:

"y = [tex]\frac{ln(x)}{ln(3)}[/tex]".

Exponential function

According to the question,

The function, y = [tex]3^x[/tex]

By switching "x" and "y" of both sides of the function,

→     x = [tex]3^y[/tex]

Now,

By taking "log" both sides,

 ln(x) = y × ln(3)

By separating the terms, we get

      y = [tex]\frac{ln(x)}{ln(3)}[/tex]

Thus the above response is correct.

Find out more information about exponential function here:

https://brainly.com/question/2456547

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