Question

What is the solution to log5(10x-1)=log5(9x=7)

Answer 1

D

Explanation:

Answer 2

`Domain:\\\\10x-1 > 0\ and\ 9x+7 > 0\\\\10x > 1\ and\ 9x > -7\\\\x > (1)/(10)\ and\ x > -(7)/(9)\Rightarrow x > (1)/(10)\\\\D=\left\x > (1)/(10)\right\\\\\\log_5(10x-1)=\log_5(9x+7)\iff10x-1=9x+7\qquad\text{add 1 to both sides}\\\\10x=9x+8\qquad\text{subtract 9x from both sides}\\\\x=8\in D\\\\Answer:\ \boxed{x=8}`