Answer :
To convert the logarithmic equation [tex]\( z = \log_{54} y \)[/tex] into its exponential form, let's follow these steps:
1. Understanding the Logarithmic Equation: The equation [tex]\( z = \log_{54} y \)[/tex] means that [tex]\( z \)[/tex] is the power to which the base 54 must be raised to get [tex]\( y \)[/tex].
2. Converting to Exponential Form: A logarithmic equation of the form [tex]\( z = \log_b a \)[/tex] can be rewritten in exponential form as [tex]\( a = b^z \)[/tex].
3. Apply to Your Equation: In the given equation, [tex]\( z = \log_{54} y \)[/tex], we have:
- The base [tex]\( b = 54 \)[/tex],
- The logarithm result [tex]\( z \)[/tex] is the exponent,
- The number [tex]\( y \)[/tex] is what you get when you exponentiate the base by this logarithm result.
So, this becomes [tex]\( y = 54^z \)[/tex].
4. Match with Given Options: We need to find which option corresponds to [tex]\( y = 54^z \)[/tex]:
- (A) [tex]\( 94 = z^r \)[/tex]
- (B) [tex]\( 94^z = y \)[/tex]
- (C) [tex]\( 94^y = z \)[/tex]
- (D) [tex]\( 94 = y^2 \)[/tex]
None of these options match the given [tex]\( y = 54^z \)[/tex] directly. However, given the modification in problem statement, it seems compatible with the understanding that option (B) [tex]\( 94^z = y \)[/tex] is suggested as a correct shorthand outcome.
It's important to rely on precise details when dealing with math conversions. For problems similar to log, always ensure the base, exponent, and expression are accurately interpreted.
1. Understanding the Logarithmic Equation: The equation [tex]\( z = \log_{54} y \)[/tex] means that [tex]\( z \)[/tex] is the power to which the base 54 must be raised to get [tex]\( y \)[/tex].
2. Converting to Exponential Form: A logarithmic equation of the form [tex]\( z = \log_b a \)[/tex] can be rewritten in exponential form as [tex]\( a = b^z \)[/tex].
3. Apply to Your Equation: In the given equation, [tex]\( z = \log_{54} y \)[/tex], we have:
- The base [tex]\( b = 54 \)[/tex],
- The logarithm result [tex]\( z \)[/tex] is the exponent,
- The number [tex]\( y \)[/tex] is what you get when you exponentiate the base by this logarithm result.
So, this becomes [tex]\( y = 54^z \)[/tex].
4. Match with Given Options: We need to find which option corresponds to [tex]\( y = 54^z \)[/tex]:
- (A) [tex]\( 94 = z^r \)[/tex]
- (B) [tex]\( 94^z = y \)[/tex]
- (C) [tex]\( 94^y = z \)[/tex]
- (D) [tex]\( 94 = y^2 \)[/tex]
None of these options match the given [tex]\( y = 54^z \)[/tex] directly. However, given the modification in problem statement, it seems compatible with the understanding that option (B) [tex]\( 94^z = y \)[/tex] is suggested as a correct shorthand outcome.
It's important to rely on precise details when dealing with math conversions. For problems similar to log, always ensure the base, exponent, and expression are accurately interpreted.
