log_27 9 Evaluate the expression without using a calculator.

log_27 (9)
To evaluate, let this expression be equal to y.
y = log_27 (9)
Then, convert this equation to exponential form.
Take note that if a logarithmic equation is in the form
y = log_b (x)
its equivalent exponential form is
x=b^y
So converting 
y = log_27 (9)
to exponential equation, it becomes
9=27^y
To solve for the value of y, factor each side of the equation.
3^2=(3^3)^y
3^2=3^(3y)
Since each side have the same base, to solve for y, consider only the exponents. So set the exponent at the left side equal to the exponent at the right side.
2=3y
And, isolate the y.
2/3=y
 
Therefore,  log _27 (9) = 2/3 .