14 3lnx21lnx 12 10log x1012 150Solution14 3lnx 2 1 lnx 3ln

14. 3ln(x)2=1ln(x)

12. 10log (x/10^-12) = 150

14 3ln(x) -2 = 1- lnx

3lnx +lnx = 3

4lnx = 3

Use the log property: ln(x^y) = yln(x)

ln(x^4) = 3

x^4 = e^3

x = e^(3/4)

12. 10 log(x/10^-12) = 150

Divide both sides by 10

log(x/10^-12) = 15

Use the log property : log(A/B) = logA - logB

logx - log(10^-12) = 15

logx +12log10 = 15

logx +12 = 15

logx = 3

x = 10^3 = 1000