What is the answer to ((64*4^{3n}+4*4^{3n+3}))/((16*4^{2n)-16^n)}= 256/3 ?

The answer to ((64*4^{3n}+4*4^{3n+3}))/((16*4^{2n)-16^n)}= 256/3 is n=1

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((644^{3n}+44^{3n+3}))/((16*4^{2n)-16^n)}= 256/3

Solution

\frac{( 64 \cdot 4 ^{3 n} + 4 \cdot 4 ^{3 n + 3} )}{( 16 \cdot 4 ^{2 n} - 1 6 ^{n} )} = \frac{256}{3}

Solution

n = 1

Solution steps

\frac{( 64 \cdot 4 ^{3 n} + 4 \cdot 4 ^{3 n + 3} )}{( 16 \cdot 4 ^{2 n} - 1 6 ^{n} )} = \frac{256}{3}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

(64 \cdot 4^{3 n} + 4 \cdot 4^{3 n + 3}) \cdot 3 = (16 \cdot 4^{2 n} - 1 6^{n}) \cdot 256

Apply exponent rules

(64 (4^{n})^{3} + 4 (4^{n})^{3} \cdot 4^{3}) \cdot 3 = (16 (4^{n})^{2} - (4^{n})^{2}) \cdot 256

Rewrite the equation with

4^{n} = u

(64 (u)^{3} + 4 (u)^{3} \cdot 4^{3}) \cdot 3 = (16 (u)^{2} - (u)^{2}) \cdot 256

Solve

(64 u^{3} + 4 u^{3} \cdot 4^{3}) \cdot 3 = (16 u^{2} - u^{2}) \cdot 256 : u = 0, u = 4

u = 0, u = 4

Substitute back

u = 4^{n},

solve for

n

Solve

4^{n} = 0 :

No Solution for

n \in R

Solve

4^{n} = 4 : n = 1

n = 1

Verify Solutions:

n = 1

True

The solution is

n = 1

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4^{x + 2} + 4^{x} = 1088

2^x=100

2^{x} = 100

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1 5^{- x + 8} = 1 4^{7 x}

5^x-24=(5^2)/(5^x)

5^{x} - 24 = \frac{5 ^{2}}{5 ^{x}}

solvefor n,a=p(1-r)^n solve for

n, a = p (1 - r)^{n}

Frequently Asked Questions (FAQ)

What is the answer to ((64*4^{3n}+4*4^{3n+3}))/((16*4^{2n)-16^n)}= 256/3 ?
The answer to ((64*4^{3n}+4*4^{3n+3}))/((16*4^{2n)-16^n)}= 256/3 is n=1
Solve for n: ((64*4^{3n}+4*4^{3n+3}))/((16*4^{2n)-16^n)}= 256/3
The solution is n=1

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to ((644^{3n}+44^{3n+3}))/((16*4^{2n)-16^n)}= 256/3 ?

Solve for n: ((644^{3n}+44^{3n+3}))/((16*4^{2n)-16^n)}= 256/3

((64*4^{3n}+4*4^{3n+3}))/((16*4^{2n)-16^n)}= 256/3

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to ((64*4^{3n}+4*4^{3n+3}))/((16*4^{2n)-16^n)}= 256/3 ?

Solve for n: ((64*4^{3n}+4*4^{3n+3}))/((16*4^{2n)-16^n)}= 256/3

((644^{3n}+44^{3n+3}))/((16*4^{2n)-16^n)}= 256/3

What is the answer to ((644^{3n}+44^{3n+3}))/((16*4^{2n)-16^n)}= 256/3 ?

Solve for n: ((644^{3n}+44^{3n+3}))/((16*4^{2n)-16^n)}= 256/3