Problem

Express the given equation in exponential form. \[ 6 \log _{46656} 6=1 \] The exponential form is (Type an equation. Use integers or fractions for any numbers in the equation.)

Solution

Step 1 :Express the given equation in exponential form. The given equation is \(6 \log _{46656} 6=1\)

Step 2 :The logarithm base b of a number x is equal to y if and only if b raised to the power of y is equal to x. In other words, if \(\log_b(x) = y\), then \(b^y = x\).

Step 3 :In the given equation, the base of the logarithm is 46656, the number inside the logarithm is 6, and the result of the logarithm operation is 1/6.

Step 4 :Therefore, the equivalent equation in exponential form should be 46656 raised to the power of 1/6 equals 6.

Step 5 :\(\boxed{46656^{\frac{1}{6}} = 6}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8M1qElaZzD/

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