What is the answer to ((8*2^n+2*2^n))/((-2^{n+1)+4*2^n)}=5^n ?

The answer to ((8*2^n+2*2^n))/((-2^{n+1)+4*2^n)}=5^n is No Solution for n\in\mathbb{R}

Solve for n: ((8*2^n+2*2^n))/((-2^{n+1)+4*2^n)}=5^n

The solution is No Solution for n\in\mathbb{R}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{( 8 \cdot 2 ^{n} + 2 \cdot 2 ^{n} )}{( - 2 ^{n + 1} + 4 \cdot 2 ^{n} )} = 5^{n}

No Solution for n \in R

Solution steps

\frac{( 8 \cdot 2 ^{n} + 2 \cdot 2 ^{n} )}{( - 2 ^{n + 1} + 4 \cdot 2 ^{n} )} = 5^{n}

Multiply both sides by

- 2^{n + 1} + 4 \cdot 2^{n}

\frac{8 \cdot 2 ^{n} + 2 \cdot 2 ^{n}}{- 2 ^{n + 1} + 4 \cdot 2 ^{n}} (- 2^{n + 1} + 4 \cdot 2^{n}) = 5^{n} (- 2^{n + 1} + 4 \cdot 2^{n})

Simplify

10 \cdot 2^{n} = 5^{n} (- 2^{n + 1} + 4 \cdot 2^{n})

Apply exponent rules

10 \cdot 2^{n} = (2^{n})^{2.32192 \dots} (- 2^{n} \cdot 2^{1} + 4 \cdot 2^{n})

Rewrite the equation with

2^{n} = u

10 u = (u)^{2.32192 \dots} (- u \cdot 2^{1} + 4 u)

Solve

10 u = u^{2.32192 \dots} (- u \cdot 2^{1} + 4 u) : u = 0

u = 0

Substitute back

u = 2^{n},

solve for

n

Solve

2^{n} = 0 :

No Solution for

n \in R

No Solution for n \in R

e^{x} - 3 x = 0

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

3^{x + 4} = 9^{x + 13}

x, 8^{2 x} \cdot 3^{- \frac{1}{2} \cdot y} = 36

\frac{243}{3125} = (\frac{3}{5})^{3 n - 1}

What is the answer to ((8*2^n+2*2^n))/((-2^{n+1)+4*2^n)}=5^n ?
The answer to ((8*2^n+2*2^n))/((-2^{n+1)+4*2^n)}=5^n is No Solution for n\in\mathbb{R}
Solve for n: ((8*2^n+2*2^n))/((-2^{n+1)+4*2^n)}=5^n
The solution is No Solution for n\in\mathbb{R}