Find the value of the following
`log_(30)1`

Answer

To find the value of \( \log_{30} 1 \), we can follow these steps:

### Step 1: Understand the Definition of Logarithm
The logarithm \( \log_b a \) is defined as the exponent to which the base \( b \) must be raised to produce the number \( a \). In other words, if \( \log_b a = c \), then \( b^c = a \).

### Step 2: Apply the Definition to Our Problem
We need to find \( \log_{30} 1 \). According to the definition, we are looking for a number \( c \) such that:
\[ 30^c = 1 \]

### Step 3: Determine the Value of \( c \)
We know that any non-zero number raised to the power of 0 equals 1. Therefore:
\[ 30^0 = 1 \]
This means that \( c = 0 \).

### Step 4: Conclude the Value of the Logarithm
Thus, we can conclude that:
\[ \log_{30} 1 = 0 \]

### Final Answer
The value of \( \log_{30} 1 \) is \( 0 \).

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