Solve the equation 9^x - 5.3^x + 4 = 0?

Question

pls dun misunderstood....
is 5.3^x not 5*3^x

Answer 1

I think you mean middle term 5*3^x

in case you put 3^x = y we get

y^2-5y + 4 = 0

(y-4)(y-1) = 0

y = 4 or 1
y=1 means x = 0
y= 4 means x = log(base 3) 4

Answer 2

9^x - 5.3^x + 4 = 0
tranpose the 4 by using additive inverse:

9^x - 5.3^x + 4 -4 = 0 -4
collect the terms:
9^x - 5.3^x = -4
factor out the x
x( 9^ - 5.3^) = -4
tranpose (9^ - 5.3^) by dividing both by it
x(9^ -5.3^) / (9^ -5.3^) = -4 / (9^ - 5.3^)
collect terms and simplify on left side of = sign
x = -4 / (9^ - 5.3^)
x = -4/ (81 - 28.09)
x = -4/ 52.91
x = -0.0756
check your work: plug the value of x in and work the equation:
9^x - 5.3^x +4=0
9^ *-0.0756 - 5.3^ * -0.0756 + 4 =0
81 * -0.0756 - 28.09 * -0.0756 + 4 = 0
-6.1236 + 2.123604 + 4 = 0
-3.99996 + 4 = 0
round off -3.99996 to one decimal place which makes it - 4.0
-4.0 +4 =0
0 = 0

Answer 3

(3²)^x - 5.3^x + 4 = 0
(3^x)² - 5.(3^x) + 4 = 0
Let 3^x = y
y² - 5y + 4 = 0
(y - 4).(y - 1) = 0
y = 4 , y = 1
3^x = 4, 3^x = 1
Take log base 3 of both sides. Denote log base 3 as log for ease of typing.
log 3^x = log 4
x log 3 = log 4
x = log 4
x = 1.262

x log 3 = 1
x = 1
ANSWERS are x = 1.262 , x = 1

Answer 4

umm..... I have trouble with math! are you smart? will you be my teacher?..

Answer 5

18.3^x