To rewrite the given exponential equation [tex]\( 3^x = 27 \)[/tex] as a logarithmic equation, let's follow these step-by-step explanations:
1. Understanding Exponential and Logarithmic Relationships:
- The general form of an exponential equation is [tex]\( a^b = c \)[/tex].
- This can be rewritten in logarithmic form as [tex]\( \log_a(c) = b \)[/tex].
- Here, [tex]\( a \)[/tex] is the base, [tex]\( c \)[/tex] is the result (or the exponent reads as [tex]\( a \)[/tex] raised to what power equals [tex]\( c \)[/tex]), and [tex]\( b \)[/tex] is the exponent.
2. Given Exponential Equation:
- The given exponential equation is [tex]\( 3^x = 27 \)[/tex].
3. Rewriting in Logarithmic Form:
- Identify the base [tex]\( a \)[/tex], which is 3.
- Identify the result [tex]\( c \)[/tex], which is 27.
- Identify the exponent [tex]\( b \)[/tex], which is [tex]\( x \)[/tex].
4. Using the Logarithmic Form:
- The equation [tex]\( 3^x = 27 \)[/tex] can be rewritten using the logarithmic form [tex]\( \log_a(c) = b \)[/tex].
- Substitute the identified values into [tex]\( \log_a(c) = b \)[/tex]:
[tex]\[
\log_3(27) = x
\][/tex]
Therefore, the logarithmic form of the given equation [tex]\( 3^x = 27 \)[/tex] is:
[tex]\[
\log_3(27) = x
\][/tex]
The correct answer is [tex]\(\boxed{\log_3 27 = x}\)[/tex].
