$$ \log _{27} 3=\square $$ (Type an integer or a fraction.)

Question

UpStudy AI · Accepted Answer

1. Write the logarithm in exponential form:
   $$
   \log_{27} 3 = x \quad \Longrightarrow \quad 27^x = 3.
   $$

2. Express 27 as a power of 3:
   $$
   27 = 3^3.
   $$
   Substitute this into the equation:
   $$
   (3^3)^x = 3.
   $$

3. Use the power of a power property:
   $$
   3^{3x} = 3^1.
   $$

4. Since the bases are the same, set the exponents equal:
   $$
   3x = 1.
   $$
   Solve for $$ x $$:
   $$
   x = \frac{1}{3}.
   $$

5. Therefore, the solution is:
   $$
   \log_{27} 3 = \frac{1}{3}.
   $$
$$ \log_{27} 3 = \frac{1}{3} $$

\( \log _{27} 3=\square \) (Type an integer or a fraction.)