Solve the equation. Use a calculator where appropriate. If the answer is irrational, round to the nearest hundredth.
-$$\log 3 x = \log 4 + \log ( x - 1 )$$
A)4
B) $- \frac { 4 } { 7 }$
C) $\frac { 3 } { 2 }$
D)-4

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can combine the right side of the equation: $\log 3x = \log 4 + \log (x - 1) = \log [4(x - 1)]$. Since the logs are equal, the arguments must be equal: $3x = 4(x - 1)$. Solving this equation gives $x = 4$.

Solve the Equation log⁡3x=log⁡4+log⁡(x−1)\log 3 x = \log 4 + \log ( x - 1 )log3x=log4+log(x−1)

Solve the Equation $\log 3 x = \log 4 + \log ( x - 1 )$