Solve the logarithmic equation. Be sure to reject any value of $x$ that is not in the domain of the original logarithmic expressions. Give the exact answer.
$\log_{5} (x + 7) + \log_{5} (x + 3) = 1$
Rewrite the given equation without logarithms. Do not solve for $x$ .

Answer

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Answer

The equation without logarithms is $5 = (x + 7) (x + 3)$

Steps

Step 1 ：Rewrite the given equation without logarithms. The equation can be rewritten as $\log_{5} ((x + 7) (x + 3)) = 1$ .

Step 2 ：Use the definition of logarithms to rewrite this equation without logarithms. The definition of logarithms states that if $\log_{b} (a) = c$ , then $b^{c} = a$ . So, we can rewrite our equation as $5^{1} = (x + 7) (x + 3)$ .

Step 3 ：The equation without logarithms is $5 = (x + 7) (x + 3)$

Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer.log5⁡(x+7)+log5⁡(x+3)=1Rewrite the given equation without logarithms. Do not solve for x.

Answer

Popular Problems

Solve the logarithmic equation. Be sure to reject any value of $x$ that is not in the domain of the original logarithmic expressions. Give the exact answer.
$\log_{5} (x + 7) + \log_{5} (x + 3) = 1$
Rewrite the given equation without logarithms. Do not solve for $x$ .