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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
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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