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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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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