What is the answer to 25^x+5^{x+1}=750 ?

The answer to 25^x+5^{x+1}=750 is x=2

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25^x+5^{x+1}=750

2 5^{x} + 5^{x + 1} = 750

x = 2

Solution steps

2 5^{x} + 5^{x + 1} = 750

Apply exponent rules

(5^{x})^{2} + 5^{x} \cdot 5^{1} = 750

Rewrite the equation with

5^{x} = u

(u)^{2} + u \cdot 5^{1} = 750

Solve

u^{2} + u \cdot 5^{1} = 750 : u = 25, u = - 30

u = 25, u = - 30

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 25 : x = 2

Solve

5^{x} = - 30 :

No Solution for

x \in R

x = 2

2^{x + 1} = 7

e^{4 x - 5} = 13

a, x^{a + 1} = \frac{1}{2}

3^{∣ x ∣ - 1} = 9

3 \cdot 2^{x} = 48