Question

Solve the equation \log(x+3)+\log x =1, inequality, or system of equations.

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asked 2021-05-16
Solve the equation \(\log(x+3)+\log x =1\), inequality, or system of equations.

Answers (1)

2021-05-17
Step 1
Given: \(\log(x+3)+\log x =1\)
Step 2
Explanation:
\(\log(x+3)+\log x =1\)
\(\Rightarrow \log_{10}(x(x+3))=1\ \ \ [\because \log(m)+\log(n)=\log(mn)]\)
\(\Rightarrow x^{2}+3x=10^{1}\ \ \ [\because \log_{a}(m)=c\ then\ m = a^{c}]\)
\(\Rightarrow x^{2}+3x-10=0\)
\(\Rightarrow x^{2}+5x-2x-10=0\)
\(\Rightarrow x(x+5)-2(x+5)=0\)
\(\Rightarrow (x+5)(x-2)=0\)
\(\Rightarrow x=-5, 2\)
\(\log\) value can't be negative
So, x=2
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