What is the answer to 5(2^{x+1})-4^x=16 ?

The answer to 5(2^{x+1})-4^x=16 is x=1,x=3

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5(2^{x+1})-4^x=16

5 (2^{x + 1}) - 4^{x} = 16

x = 1, x = 3

Solution steps

5 (2^{x + 1}) - 4^{x} = 16

Apply exponent rules

5 \cdot 2^{x} \cdot 2^{1} - (2^{x})^{2} = 16

Rewrite the equation with

2^{x} = u

5 u \cdot 2^{1} - (u)^{2} = 16

Solve

5 u \cdot 2^{1} - u^{2} = 16 : u = 2, u = 8

u = 2, u = 8

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 2 : x = 1

Solve

2^{x} = 8 : x = 3

x = 1, x = 3

4 9^{x + 3} = 7^{x^{2} - 3 x - 8}

1 + 9^{x} = 3^{x + 1} + 3^{x - 1}

\frac{9 ^{x}}{9 ^{3}} = 9^{5}

6^{x} = 12

3^{x + 1} = 8

What is the answer to 5(2^{x+1})-4^x=16 ?
The answer to 5(2^{x+1})-4^x=16 is x=1,x=3
Solve for x: 5(2^{x+1})-4^x=16
The solution is x=1,x=3