Answer :
Let's solve the given equation step-by-step:
[tex]\[ 2 \log x - \log 4 = 0 \][/tex]
Step 1: Move [tex]\(\log 4\)[/tex] to the right side of the equation
[tex]\[ 2 \log x = \log 4 \][/tex]
Step 2: Divide both sides by 2 to isolate [tex]\(\log x\)[/tex]
[tex]\[ \log x = \frac{\log 4}{2} \][/tex]
Step 3: Recall that [tex]\(\frac{\log 4}{2}\)[/tex] is the same as [tex]\(\log (4^{1/2})\)[/tex], because of the power rule for logarithms [tex]\(\log(a^b) = b \log a\)[/tex]
[tex]\[ \log x = \log (4^{1/2}) \][/tex]
Step 4: Simplify [tex]\(4^{1/2}\)[/tex] to [tex]\(2\)[/tex], because the square root of 4 is 2
[tex]\[ \log x = \log 2 \][/tex]
Step 5: Since the logarithm function is one-to-one, if [tex]\(\log x = \log 2\)[/tex], then
[tex]\[ x = 2 \][/tex]
Thus, the solution is
[tex]\[ \boxed{2.0} \][/tex]
[tex]\[ 2 \log x - \log 4 = 0 \][/tex]
Step 1: Move [tex]\(\log 4\)[/tex] to the right side of the equation
[tex]\[ 2 \log x = \log 4 \][/tex]
Step 2: Divide both sides by 2 to isolate [tex]\(\log x\)[/tex]
[tex]\[ \log x = \frac{\log 4}{2} \][/tex]
Step 3: Recall that [tex]\(\frac{\log 4}{2}\)[/tex] is the same as [tex]\(\log (4^{1/2})\)[/tex], because of the power rule for logarithms [tex]\(\log(a^b) = b \log a\)[/tex]
[tex]\[ \log x = \log (4^{1/2}) \][/tex]
Step 4: Simplify [tex]\(4^{1/2}\)[/tex] to [tex]\(2\)[/tex], because the square root of 4 is 2
[tex]\[ \log x = \log 2 \][/tex]
Step 5: Since the logarithm function is one-to-one, if [tex]\(\log x = \log 2\)[/tex], then
[tex]\[ x = 2 \][/tex]
Thus, the solution is
[tex]\[ \boxed{2.0} \][/tex]
