Make into one log function:
2logx-log4-log3+logx
2logx-log4-log3+logx
3 log x - log 4 - log 3
3 log x - log 12
log (x^3/12)
To simplify the expression "2logx - log4 - log3 + logx" into a single logarithm, we will use the properties of logarithms.
1. Start by using the product rule of logarithms, which states that log(a) + log(b) = log(ab). Apply this rule to simplify "2logx + logx".
2logx + logx = log(x^2) + log(x) = log(x^2 * x) = log(x^3)
2. Next, use the quotient rule of logarithms, which states that log(a) - log(b) = log(a/b). Apply this rule to simplify "-log4 - log3".
-log4 - log3 = log(1/4) - log(3) = log(1/4 * 1/3) = log(1/12)
3. Now, combine the simplified expressions obtained from step 1 and step 2.
2logx - log4 - log3 + logx = log(x^3) - log(1/12)
4. Finally, use the quotient rule to subtract the logarithms.
log(x^3) - log(1/12) = log((x^3)/(1/12)) = log(12x^3)
Therefore, the expression "2logx - log4 - log3 + logx" simplifies to "log(12x^3)" as a single logarithm.