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Rewrite the logarithmic equation as an exponential equation. You do not need to solve for [tex]\( x \)[/tex].

[tex]\[ \log_{(x+7)}(5x) = 5x \][/tex]

Sagot :

GinnyAnswer
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.
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