22

solve for x.

(using exponentials/logarithms to solve.)

a) x = -7/4
b) x = 4/7
c) x = 3/7
d) x = -4/7

4³ ⁻ ˣ . (1/8)²ˣ ⁺ ⁵ = 16ˣ ⁺ ³

4 = 2²,          8 = 2³,  16 = 2⁴

(2²)³ ⁻ ˣ . (1/2³)²ˣ ⁺ ⁵ = (2⁴)ˣ ⁺ ³

(2²)³ ⁻ ˣ . (2⁻³)²ˣ ⁺ ⁵ = (2⁴)ˣ ⁺ ³

Multiply out the powers.

2²⁽³ ⁻ ˣ⁾. 2⁻³⁽²ˣ ⁺ ⁵⁾ = 2⁴⁽ˣ ⁺ ³⁾

2*(3 - x) = 2*3 - 2*x = 6 - 2x

-3*(2x +5) = -3*2x - 3*5 = -6x - 15

4(x +3) = 4*x + 4*3 = 4x + 12
 

2²⁽³ ⁻ ˣ⁾. 2⁻³⁽²ˣ ⁺ ⁵⁾ = 2⁴⁽ˣ ⁺ ³⁾

2⁶ ⁻ ²ˣ . 2⁻⁶ˣ ⁻ ¹⁵ = 2⁴ˣ ⁺ ¹²

On the left hand side we add the powers, because it is a multiplication process.

2⁶ ⁻ ²ˣ ⁺ ⁽⁻⁶ˣ ⁻ ¹⁵⁾ = 2⁴ˣ ⁺ ¹²

Since the bases of the equation are the same, hence the powers are the same.

6 - 2x + (-6x -15) = 4x +12

6 - 2x - 6x - 15 = 4x + 12

-2x - 6x - 4x = 12 - 6 + 15

-12x = 21

Divide by -12.

x =21/-12,          cancel through by 3.

x = -7/4

I hope this helped.

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.