What is the answer to 5^{6x+1}-6*5^{3x}+1=0 ?

The answer to 5^{6x+1}-6*5^{3x}+1=0 is x=0,x=-1/3

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5^{6x+1}-6*5^{3x}+1=0

5^{6 x + 1} - 6 \cdot 5^{3 x} + 1 = 0

x = 0, x = - \frac{1}{3}

Solution steps

5^{6 x + 1} - 6 \cdot 5^{3 x} + 1 = 0

Apply exponent rules

(5^{x})^{6} \cdot 5^{1} - 6 (5^{x})^{3} + 1 = 0

Rewrite the equation with

5^{x} = u

(u)^{6} \cdot 5^{1} - 6 (u)^{3} + 1 = 0

Solve

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 1 : x = 0

Solve

x = 0, x = - \frac{1}{3}

(2)^{x} = 16

3^{x} - 3^{1 - x} = 2

e^{x} = e^{4 - x}

\frac{3 ^{x}}{9 ^{2 x + 3}} = 1

6^{x} = 6

What is the answer to 5^{6x+1}-6*5^{3x}+1=0 ?
The answer to 5^{6x+1}-6*5^{3x}+1=0 is x=0,x=-1/3
Solve for x: 5^{6x+1}-6*5^{3x}+1=0
The solution is x=0,x=-1/3