Question

Log10(3x-1)-log10(2)=3

Answer 1

Log10(3x-1)-log10(2) = 3

log10 [3x-1)/2 = 3

(3x - 1) / 2 = 10^3

3x - 1 = 2000

x = 2001 / 3

= 667 Answer

Answer 2

`\log_(10)x=\log x`

`The\ domain:\\3x-1 > 0\to x > (1)/(3)\to x\in\left((1)/(3),\ \infty\right)\\\\\log(3x-1)-\log2=3\ \ \ \ \boxed{\text{use}\ \log_a(b)/(c)=\log_ab-\log_ac}\\\\\log(3x-1)/(2)=3\ \ \ \ \boxed{\text{use}\ \log_ab=c\iff a^c=b}\\\\(3x-1)/(2)=10^3\\\\(3x-1)/(2)=1000\ \ \ \ \ |\cdot2\\\\3x-1=2000\ \ \ \ |+1\\\\3x=2001\ \ \ \ |:3\\\\x=667 > (1)/(3)\\\\Answer:\ \boxed{x=667}`