Consider the equation log(3x - 1) = log28. Explain why 3x - 1 is not equal to 8. Describe the steps you would take to solve the equation, and state what 3x - 1 is equal to

Accepted Solution

Using logarithms, it is found that since both sides have different bases, 3x - 1 is not equal to 8.Using change of base, it is found that 3x - 1 is equals to [tex]\frac{\log{8}}{\log{2}}[/tex]The equation given is:[tex]\log{(3x - 1)} = \log_{2}{8}[/tex]The logarithms at each side of the equality have different bases, hence 3x - 1 is not equal to 8.Making the conversion of the right side to base 10, we have that:[tex]\log_{2}{8} = \frac{\log{8}}{\log{2}}[/tex]Hence:[tex]\log{(3x - 1)} = \frac{\log{8}}{\log{2}}[/tex]3x - 1 is equals to [tex]\frac{\log{8}}{\log{2}}[/tex]A similar problem is given at