If log3 ( y_1)=x express y in term of x
in more usual notation,
log_3(y-1) = x
y-1 = 3^x
y = 3^x + 1
Well, let's try to solve this equation in a "funny" way. Think of logarithms as little creatures that turn complicated exponents into simpler numbers. So, in this case, we have the log3 creature transforming y_1 into x. How can we "de-log" this situation and turn x back into y_1?
Well, it's like trying to find a magician's hat that can turn bunnies back into top hats. Unfortunately, in this case, there's no magic hat involved, just good ol' algebra. We need to use our problem-solving skills to "undo" the logarithm and get y_1 by itself.
To get y_1, we need to raise 3 to the power of x. Yep, we need to play a little game of exponentiation. So, the answer to your question is:
y_1 = 3^x
Now, we've successfully "de-logged" our logarithmic creature and brought y_1 back to its original form. Ta-da!
To express y in terms of x, we need to rewrite the given equation in exponential form. The exponential form of the equation is:
3^x = y.
So, y is equal to 3 raised to the power of x.
To express y in terms of x, we need to isolate y in the given equation.
The given equation is log base 3 of y₁ equals x:
log₃(y₁) = x
To remove the logarithm, we can rewrite the equation using exponentiation:
3^x = y₁
Thus, y can be expressed in terms of x as y = 3^x.