Write the logarithmic equation $\log _{6} x=5$ in exponential form.
The logarithmic equation written as an exponential equation is
Answer
Final Answer: The logarithmic equation \(\log _{6} x=5\) in exponential form is \(6^5 = x\), which simplifies to \(x = \boxed{7776}\).
Step 1 ：The logarithmic equation \(\log _{6} x=5\) can be converted to exponential form by using the definition of a logarithm.
Step 2 ：The base of the logarithm becomes the base of the power, the right side of the equation becomes the exponent, and the result is the number inside the logarithm.
Step 3 ：So, the exponential form of the equation is \(6^5 = x\).
Step 4 ：By calculating, we find that \(x = 7776.0\).
Step 5 ：Final Answer: The logarithmic equation \(\log _{6} x=5\) in exponential form is \(6^5 = x\), which simplifies to \(x = \boxed{7776}\).
