What is the answer to 2^{2x+3}-57=65(2^x-1) ?

The answer to 2^{2x+3}-57=65(2^x-1) is x=3,x=-3

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2^{2x+3}-57=65(2^x-1)

2^{2 x + 3} - 57 = 65 (2^{x} - 1)

x = 3, x = - 3

Solution steps

2^{2 x + 3} - 57 = 65 (2^{x} - 1)

Apply exponent rules

(2^{x})^{2} \cdot 2^{3} - 57 = 65 (2^{x} - 1)

Rewrite the equation with

2^{x} = u

(u)^{2} \cdot 2^{3} - 57 = 65 (u - 1)

Solve

u^{2} \cdot 2^{3} - 57 = 65 (u - 1) : u = 8, u = \frac{1}{8}

u = 8, u = \frac{1}{8}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = \frac{1}{8} : x = - 3

x = 3, x = - 3

4^{2 x} + 4^{2 x - 1} = 4

3^{x - 2} = 9 a^{x - 4}

x, 2^{5 x} + 2^{8 y} = 2^{13 z}

n, x^{n} = 0

x, q (3^{2 x + 1}) = 54

What is the answer to 2^{2x+3}-57=65(2^x-1) ?
The answer to 2^{2x+3}-57=65(2^x-1) is x=3,x=-3
Solve for x: 2^{2x+3}-57=65(2^x-1)
The solution is x=3,x=-3