To rewrite the given logarithmic equation [tex]\(\log_{(x+7)}(5x) = 5x\)[/tex] as an exponential equation, follow these steps:
1. Understand the logarithmic form:
[tex]\[
\log_{a}(b) = c
\][/tex]
means
[tex]\[
a^c = b
\][/tex]
2. Here, [tex]\(a = (x + 7)\)[/tex], [tex]\(b = 5x\)[/tex], and [tex]\(c = 5x\)[/tex].
3. Substitute these values into the exponential form:
[tex]\[
(x + 7)^{5x} = 5x
\][/tex]
Thus, the logarithmic equation [tex]\(\log_{(x+7)}(5x) = 5x\)[/tex] can be rewritten in its exponential form as:
[tex]\[
(x + 7)^{5x} = 5x
\][/tex]
This is the exponential expression equivalent to the given logarithmic equation.
