What is the answer to 25^{x+1}+3*5^{x+2}-16=0 ?

The answer to 25^{x+1}+3*5^{x+2}-16=0 is x=-1

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25^{x+1}+3*5^{x+2}-16=0

2 5^{x + 1} + 3 \cdot 5^{x + 2} - 16 = 0

x = - 1

Solution steps

2 5^{x + 1} + 3 \cdot 5^{x + 2} - 16 = 0

Apply exponent rules

(5^{x})^{2} \cdot 5^{2} + 3 \cdot 5^{x} \cdot 5^{2} - 16 = 0

Rewrite the equation with

5^{x} = u

(u)^{2} \cdot 5^{2} + 3 u \cdot 5^{2} - 16 = 0

Solve

u^{2} \cdot 5^{2} + 3 u \cdot 5^{2} - 16 = 0 : u = \frac{1}{5}, u = - \frac{16}{5}

u = \frac{1}{5}, u = - \frac{16}{5}

Substitute back

u = 5^{x},

solve for

x

Solve

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

Solve

5^{x} = - \frac{16}{5} :

No Solution for

x \in R

x = - 1

2. 5^{- 4 x} = 6.4

15 = 3 (8)^{- x - 4}

3^{2 x} + 3^{x + 1} - 4 = 0

8^{x} = 1 6^{x}

6^{- 2 x} = 6^{2 - 3 x}

What is the answer to 25^{x+1}+3*5^{x+2}-16=0 ?
The answer to 25^{x+1}+3*5^{x+2}-16=0 is x=-1
Solve for x: 25^{x+1}+3*5^{x+2}-16=0
The solution is x=-1