4) Resuelve las siguientes ecuaciones 1) \( \log x+\log 4=\log 1 \)

Solve the equation \( \log(x)+\log(4)=\log(1) \). Solve the equation by following steps: - step0: Solve for \(x\): \(\log_{10}{\left(x\right)}+\log_{10}{\left(4\right)}=\log_{10}{\left(1\right)}\) - step1: Find the domain: \(\log_{10}{\left(x\right)}+\log_{10}{\left(4\right)}=\log_{10}{\left(1\right)},x>0\) - step2: Simplify: \(\log_{10}{\left(x\right)}+2\log_{10}{\left(2\right)}=0\) - step3: Move the constant to the right side: \(\log_{10}{\left(x\right)}=0-2\log_{10}{\left(2\right)}\) - step4: Remove 0: \(\log_{10}{\left(x\right)}=-2\log_{10}{\left(2\right)}\) - step5: Rewrite the logarithm: \(\log_{10}{\left(x\right)}=\log_{10}{\left(2^{-2}\right)}\) - step6: Rewrite the expression: \(x=2^{-2}\) - step7: Simplify: \(x=\frac{1}{4}\) - step8: Check if the solution is in the defined range: \(x=\frac{1}{4},x>0\) - step9: Find the intersection: \(x=\frac{1}{4}\) La solución de la ecuación \( \log x + \log 4 = \log 1 \) es \( x = \frac{1}{4} \) o \( x = 0.25 \).