Question 867303: Solve
a) 5^2x + 5^x - 6 = 0 let y = 5^x
b) 9^x - 5(3^x)+6 = 0 let y = 3^x
Can you please help me out? Thanks so much in advance:) Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Solve
a) 5^2x + 5^x - 6 = 0 let y = 5^x
b) 9^x - 5(3^x)+6 = 0 let y = 3^x
***
y=5^x
y^2=5^2x
..
a) 5^2x + 5^x - 6 = 0
y^2+y-6=0
(y+3)(y-2)=0
..
y=-3=5^x
no solution:
5^x>0
or
y=2=5^x
log2=xlog5
x=log2/log5≈0.4306…
..
y=3^x
y^2=3^2x
9^x=3^2x
..
b) 9^x - 5(3^x)+6 = 0 let y = 3^x
3^2x - 5(3^x)+6 = 0 let y = 3^x
y^2-5y+6=0
(y-2)(y-3)=0
..
y=2=3^x
log2=xlog3
x=log2/log3≈0.6309…
or
x=3=3^x
log3/xlog3
x=log3/log3=1
(