What is the answer to 6^{2n+1}+6^2=6^n+6^{n+3} ?

The answer to 6^{2n+1}+6^2=6^n+6^{n+3} is n=2,n=-1

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6^{2n+1}+6^2=6^n+6^{n+3}

6^{2 n + 1} + 6^{2} = 6^{n} + 6^{n + 3}

n = 2, n = - 1

Solution steps

6^{2 n + 1} + 6^{2} = 6^{n} + 6^{n + 3}

Apply exponent rules

(6^{n})^{2} \cdot 6^{1} + 6^{2} = 6^{n} + 6^{n} \cdot 6^{3}

Rewrite the equation with

6^{n} = u

(u)^{2} \cdot 6^{1} + 6^{2} = u + u \cdot 6^{3}

Solve

u^{2} \cdot 6^{1} + 6^{2} = u + u \cdot 6^{3} : u = 36, u = \frac{1}{6}

u = 36, u = \frac{1}{6}

Substitute back

u = 6^{n},

solve for

n

Solve

6^{n} = 36 : n = 2

Solve

6^{n} = \frac{1}{6} : n = - 1

n = 2, n = - 1

x^{l o g_{10} (4 x)} = 256

i, x^{i} = 2

9^{x} = 2 7^{x}

(\frac{1}{3})^{2 x + 5} = 2 7^{1 - x}

What is the answer to 6^{2n+1}+6^2=6^n+6^{n+3} ?
The answer to 6^{2n+1}+6^2=6^n+6^{n+3} is n=2,n=-1
Solve for n: 6^{2n+1}+6^2=6^n+6^{n+3}
The solution is n=2,n=-1