Question

Solve for x using technology 2 log 3(x-1)=log(4 x 2-25)

Answer 1

2 log 3(x-1)=log(4 x 2-25)
1.  Determine the domain.  Since the input to the log function cannot be zero or negative, 4x^2-25 must be ≥ 0.  Thus, x^2 must be >0, or x>0.  Same domain applies to log (3(x-1); x must be > 0.
2.  Rewrite 2 log 3(x-1) as log 3(x-1)^2.
3.  Then we have log 3(x-1)^2 = log(4 x 2-25).  We can discard the operator "log" from both sides:   3(x-1)^2 = 4 x 2-25.  There are various ways in which to solve this.  Since you're supposed to "use technology," 
graph y = 3(x-1)^2 and y = 4x^2 - 25 on the same set of axes.  Determine, using visual estimation or your calculator's tools, the value or values of x that satisfy this equation.  My result was x=3, y =11.