Answer :
To convert a logarithmic equation to its exponential form, we need to understand the relationship between logarithms and exponents. In general, when you have a logarithmic equation of the form [tex]\( z = \log_b(y) \)[/tex], it can be rewritten in exponential form as [tex]\( b^z = y \)[/tex].
Let's apply this to the given problem:
You have the equation:
[tex]\[ z = \log_{94}(y) \][/tex]
Here, the base [tex]\( b \)[/tex] is 94, the logarithm [tex]\( z \)[/tex] is the exponent, and [tex]\( y \)[/tex] is the result. To express this in exponential form, follow these steps:
1. Identify the base of the logarithm, which is 94.
2. Recognize that the logarithm indicates the power to which the base must be raised to obtain the number [tex]\( y \)[/tex].
3. Rewrite the equation by setting the base (94) raised to the power of the logarithm ([tex]\( z \)[/tex]) equal to [tex]\( y \)[/tex].
So, the exponential form of the equation [tex]\( z = \log_{94}(y) \)[/tex] is:
[tex]\[ 94^z = y \][/tex]
Based on the options provided:
A) [tex]\( 94 = z^y \)[/tex]
B) [tex]\( 94^z = y \)[/tex]
C) [tex]\( 94^y = z \)[/tex]
D) [tex]\( 94 = y^2 \)[/tex]
The correct choice that matches [tex]\( 94^z = y \)[/tex] is option B.
Let's apply this to the given problem:
You have the equation:
[tex]\[ z = \log_{94}(y) \][/tex]
Here, the base [tex]\( b \)[/tex] is 94, the logarithm [tex]\( z \)[/tex] is the exponent, and [tex]\( y \)[/tex] is the result. To express this in exponential form, follow these steps:
1. Identify the base of the logarithm, which is 94.
2. Recognize that the logarithm indicates the power to which the base must be raised to obtain the number [tex]\( y \)[/tex].
3. Rewrite the equation by setting the base (94) raised to the power of the logarithm ([tex]\( z \)[/tex]) equal to [tex]\( y \)[/tex].
So, the exponential form of the equation [tex]\( z = \log_{94}(y) \)[/tex] is:
[tex]\[ 94^z = y \][/tex]
Based on the options provided:
A) [tex]\( 94 = z^y \)[/tex]
B) [tex]\( 94^z = y \)[/tex]
C) [tex]\( 94^y = z \)[/tex]
D) [tex]\( 94 = y^2 \)[/tex]
The correct choice that matches [tex]\( 94^z = y \)[/tex] is option B.
