4^x-3.2^x+3+128=0 then x=
Answers
Step-by-step explanation:
4 x −3(2 x+3)+128=0
⇒(2 x ) 2−24.2 x+128=0
⇒y 2−24y+128=0
⇒y 2 −8y−16y+128=0
⇒y(y−8)−16(y−8)=0
⇒(y−8)(y−16)=0
y=8 or y=16
x=3x=4
nothing more to say thank you
Concept:
The formula for an exponential function is f (x) = aˣ, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x). The roots of the quadratic equation are the values of x that fulfil the equation (α, β).
It is a given that the quadratic equation has two roots. Roots might have either a real or imaginary nature.
Given:
4ˣ −3(2ˣ⁺³)+128=0
Find:
Find x
Solution:
4ˣ −3(2ˣ⁺³)+128=0
⇒(2ˣ)²−3.2ˣ.8+128=0
Let, 2ˣ=y
⇒y²−24y+128=0
⇒y² −8y−16y+128=0
⇒y(y−8)−16(y−8)=0
⇒(y−8)(y−16)=0
y=8 or y=16
when, 2ˣ=8
⇒x=3
And when, 2ˣ=16
⇒x=4
x=3x,4
Therefore, the roots of the equation are 3,4
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