What is the answer to 5^{2x+1}=6(5^x)-1 ?

The answer to 5^{2x+1}=6(5^x)-1 is x=0,x=-1

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5^{2x+1}=6(5^x)-1

5^{2 x + 1} = 6 (5^{x}) - 1

x = 0, x = - 1

Solution steps

5^{2 x + 1} = 6 (5^{x}) - 1

Apply exponent rules

(5^{x})^{2} \cdot 5^{1} = 6 \cdot 5^{x} - 1

Rewrite the equation with

5^{x} = u

(u)^{2} \cdot 5^{1} = 6 u - 1

Solve

u^{2} \cdot 5^{1} = 6 u - 1 : u = 1, u = \frac{1}{5}

u = 1, u = \frac{1}{5}

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 1 : x = 0

Solve

5^{x} = \frac{1}{5} : x = - 1

x = 0, x = - 1

3^{4 - x^{2}} = \frac{1}{9}

2 e^{x} = 1

2^{- m} = 2^{3 m - 3}

5^{2 x} - 6 (5^{x}) + 5 = 0

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

What is the answer to 5^{2x+1}=6(5^x)-1 ?
The answer to 5^{2x+1}=6(5^x)-1 is x=0,x=-1
Solve for x: 5^{2x+1}=6(5^x)-1
The solution is x=0,x=-1