Respuesta :
The bases are not the same, so you cannot set 3x - 1 equal to 8.
You can evaluate the logarithm on the right side of the equation to get 3.
You can use the definition of a logarithm to write 3x - 1 = 1000.
Answer: The solution of the given equation is [tex]x=333\dfrac{2}{3}[/tex] and the value of (3x - 1) is 1000.
Step-by-step explanation: We are given to describe the steps in solving the following logarithmic equation:
[tex]\log(3x-1)=\log_28.[/tex]
Also, we are to find the value of [tex](3x-1).[/tex]
We will be using the following logarithmic properties:
[tex](i)~\log_ba=x~~~\Rightarrow a=b^x,\\\\(ii)~\log_ba=\dfrac{\log a}{\log b},\\\\(iii)~\log a^b=b\log a.[/tex]
We note here that if the base of logarithm is not mentioned, then we assume it to be 10.
The solution is as follows:
[tex]\log(3x-1)=\log_28\\\\\Rightarrow \log(3x-1)=\dfrac{\log8}{\log2}\\\\\Rightarrow log(3x-1)=\dfrac{\log2^3}{\log2}\\\\\Rightarrow \log(3x-1)=\dfrac{3\log2}{\log2}\\\\\Rightarrow \log(3x-1)=3\\\\\Rightarrow 3x-1=10^3\\\\\Rightarrow 3x-1=1000\\\\\Rightarrow 3x=1001\\\\\Rightarrow x=\dfrac{1001}{3}\\\\\Rightarrow x=333\dfrac{2}{3}.[/tex]
Thus, the solution of the given equation is [tex]x=333\dfrac{2}{3}[/tex] and the value of (3x - 1) is 1000.
