solve following equation (log x)(2 log x+5) = 12 -> solution set is:

Question

1. Check each proposed solution by direct substitution or with a graphing utility.

Answer 1

2log²x + 5logx - 12 = 0; (2logx - 3)(logx + 4) = 0; 2logx - 3 = 0 or logx + 4 = 0; logx = 3/2, x = 10^3/2 = 10·10^1/2;

^{or logx = - 4, x = 10^(- 4) = 0.0001}

^{Answer: x = 10 · 10^(1/2); or x = 0.0001:}

Answer 2

1) distribute the log(x): 2log²x + 5logx = 12 or 2log²x + 5logx - 12 = 0

2) Let y = log x: 2y² + 5y -12 = 0

3) Solve for roots using quadratic formula or factoring: (2y - 3)(y + 4) = 0

4) Roots are 3/2 and -4

5) y = log x or 10^y = x = 10^3/2 or 10^-4

Take care.