What is the answer to 729*(2^{n-5})^n-64*(3^n)^{n-5}=0 ?

The answer to 729*(2^{n-5})^n-64*(3^n)^{n-5}=0 is

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729(2^{n-5})^n-64(3^n)^{n-5}=0

Solution

729 \cdot (2^{n - 5})^{n} - 64 \cdot (3^{n})^{n - 5} = 0

Solution

n = \frac{5 ln ( 2 ) - 5 ln ( 3 ) + 49 ln ^{2} ( 2 ) - 98 ln ( 3 ) ln ( 2 ) + 49 ln ^{2} ( 3 )}{2 ( ln ( 2 ) - ln ( 3 ) )}, n = - \frac{5 ln ( 3 ) - 5 ln ( 2 ) + 49 ln ^{2} ( 2 ) - 98 ln ( 3 ) ln ( 2 ) + 49 ln ^{2} ( 3 )}{2 ( ln ( 2 ) - ln ( 3 ) )}

Decimal Notation

n = - 1, n = 6

Solution steps

729 (2^{n - 5})^{n} - 64 (3^{n})^{n - 5} = 0

Factor

729 (2^{n - 5})^{n} - 64 (3^{n})^{n - 5} : 729 \cdot 2^{n (n - 5)} - 64 \cdot 3^{n (n - 5)}

729 \cdot 2^{n (n - 5)} - 64 \cdot 3^{n (n - 5)} = 0

Add

64 \cdot 3^{n (n - 5)}

to both sides

729 \cdot 2^{n (n - 5)} - 64 \cdot 3^{n (n - 5)} + 64 \cdot 3^{n (n - 5)} = 0 + 64 \cdot 3^{n (n - 5)}

Simplify

729 \cdot 2^{n (n - 5)} = 64 \cdot 3^{n (n - 5)}

Apply exponent rules

ln (729) + n (n - 5) ln (2) = ln (64) + n (n - 5) ln (3)

Solve

ln (729) + n (n - 5) ln (2) = ln (64) + n (n - 5) ln (3) : n = \frac{5 ln ( 2 ) - 5 ln ( 3 ) + 49 ln ^{2} ( 2 ) - 98 ln ( 3 ) ln ( 2 ) + 49 ln ^{2} ( 3 )}{2 ( ln ( 2 ) - ln ( 3 ) )}, n = - \frac{5 ln ( 3 ) - 5 ln ( 2 ) + 49 ln ^{2} ( 2 ) - 98 ln ( 3 ) ln ( 2 ) + 49 ln ^{2} ( 3 )}{2 ( ln ( 2 ) - ln ( 3 ) )}

n = \frac{5 ln ( 2 ) - 5 ln ( 3 ) + 49 ln ^{2} ( 2 ) - 98 ln ( 3 ) ln ( 2 ) + 49 ln ^{2} ( 3 )}{2 ( ln ( 2 ) - ln ( 3 ) )}, n = - \frac{5 ln ( 3 ) - 5 ln ( 2 ) + 49 ln ^{2} ( 2 ) - 98 ln ( 3 ) ln ( 2 ) + 49 ln ^{2} ( 3 )}{2 ( ln ( 2 ) - ln ( 3 ) )}

Popular Examples

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8^x=16^{-1}*sqrt(32^x)

8^{x} = 1 6^{- 1} \cdot 3 2^{x}

1/64 =(1/2)^{n-1}

\frac{1}{64} = (\frac{1}{2})^{n - 1}

3^{2x+1}=5^{2x+1}

3^{2 x + 1} = 5^{2 x + 1}

10^x=-2

1 0^{x} = - 2

Frequently Asked Questions (FAQ)

What is the answer to 729*(2^{n-5})^n-64*(3^n)^{n-5}=0 ?
The answer to 729*(2^{n-5})^n-64*(3^n)^{n-5}=0 is
Solve for n: 729*(2^{n-5})^n-64*(3^n)^{n-5}=0
The solution is

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to 729(2^{n-5})^n-64(3^n)^{n-5}=0 ?

Solve for n: 729(2^{n-5})^n-64(3^n)^{n-5}=0

729*(2^{n-5})^n-64*(3^n)^{n-5}=0

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to 729*(2^{n-5})^n-64*(3^n)^{n-5}=0 ?

Solve for n: 729*(2^{n-5})^n-64*(3^n)^{n-5}=0

729(2^{n-5})^n-64(3^n)^{n-5}=0

What is the answer to 729(2^{n-5})^n-64(3^n)^{n-5}=0 ?

Solve for n: 729(2^{n-5})^n-64(3^n)^{n-5}=0