To convert the logarithmic equation [tex]\( x = \log_4 \frac{y}{5} \)[/tex] to its exponential form, follow these steps:
1. Start with the given logarithmic equation:
[tex]\[
x = \log_4 \frac{y}{5}
\][/tex]
2. Recall the definition of a logarithm. If [tex]\( x = \log_b a \)[/tex], then [tex]\( b^x = a \)[/tex]. Using this definition, we can rewrite the equation in its exponential form. Here, [tex]\( b = 4 \)[/tex] and [tex]\( a = \frac{y}{5} \)[/tex].
3. Therefore, we convert the logarithmic form to exponential form:
[tex]\[
4^x = \frac{y}{5}
\][/tex]
4. To solve for [tex]\( y \)[/tex], multiply both sides of the equation by 5:
[tex]\[
y = 5 \cdot 4^x
\][/tex]
So, the exponential form of the given logarithmic equation [tex]\( x = \log_4 \frac{y}{5} \)[/tex] is:
[tex]\[
y = 5 \cdot 4^x
\][/tex]
Hence, the correct answer is:
[tex]\[
y = 5 \cdot 4^x
\][/tex]
