To convert the given logarithmic equation [tex]\(x = \log_7(y - 4)\)[/tex] into exponential form, we start by understanding the basic relationship between logarithms and exponents.
The logarithmic equation [tex]\( \log_b(a) = c \)[/tex] is equivalent to the exponential equation [tex]\( b^c = a \)[/tex].
Applying this principle to our specific question:
Given:
[tex]\[ x = \log_7(y - 4) \][/tex]
This means that:
[tex]\[ 7^x = y - 4 \][/tex]
We want to solve for [tex]\( y \)[/tex]:
1. Start with the exponential form derived from the logarithmic equation:
[tex]\[ 7^x = y - 4 \][/tex]
2. To isolate [tex]\( y \)[/tex], add 4 to both sides of the equation:
[tex]\[ 7^x + 4 = y \][/tex]
3. Therefore, we can rewrite the equation as:
[tex]\[ y = 7^x + 4 \][/tex]
Thus, the correct exponential form of the given logarithmic equation [tex]\( x = \log_7(y - 4) \)[/tex] is:
[tex]\[ y = 7^x + 4 \][/tex]
So, the correct answer is:
[tex]\[ y = 7^x + 4 \][/tex]
