If x=3^y, what to you think you would write to solve for y? Explain

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justaguide eNotes educator | Certified Educator

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If x = 3^y, we can solve the equation for y in many ways.

One of them would be by using logarithms.

Take the logarithm of any base of both the side.

x = 3^y

= log x = log ( 3^y)

use the relation log x^y = y*log x

=> log x = y * log 3

=> y = log x / log 3

On substituting the value of x we get the value of y.

y can be determined by using y = log x / log 3

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giorgiana1976 | Student

To solve the equation for y, we'll have to take natural or decimal logarithms both sides.

Why? Only using the power properties of logarithms, we'll get down the variable y from superscript position, where it is actually.

ln x = ln (3^y)

We'll use the power property:

ln x = y*ln 3

Now, we'll use the symmetrical property:

y*ln 3 = ln x

We'll divide by ln 3:

y = ln x/ ln 3

The required y is: y = ln x/ ln 3.

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