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 $\boxed{5=(x+7)(x+3)}$

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 $\boxed{5=(x+7)(x+3)}$

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.\[\log _{5}(x+7)+\log _{5}(x+3)=1\]Rewrite 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 $x$.