#26 + 27

#26. Solve for x: log(2x)+log(x+5)=2

log(2x*(x+5))=2 -----------------------using formula: loga+logb=log(a*b).

2x^2+10x=100-------------------------using theory: loga=b, 10^b=a.

x=-10 and 5.

check: x cannot be -10, so x=5.-----------------using theory: loga=b only if a > 0 .

#27. ab^t=ae^rt

b^t=e^rt-----------------------divide a on both sides.

ln(b^t)=ln(e^rt)----------------take ln on both sides.

ln(b^t)=rt----------------------using theory: ln(e^a)=a.

t ln b=rt------------------------ln (a^b)=b ln a.

lnb=r---------------------------divide t on both sides.