What is the answer to 25^x-3*5^x=10 ?

The answer to 25^x-3*5^x=10 is x=1

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25^x-3*5^x=10

2 5^{x} - 3 \cdot 5^{x} = 10

x = 1

Solution steps

2 5^{x} - 3 \cdot 5^{x} = 10

Apply exponent rules

(5^{x})^{2} - 3 \cdot 5^{x} = 10

Rewrite the equation with

5^{x} = u

(u)^{2} - 3 u = 10

Solve

u^{2} - 3 u = 10 : u = 5, u = - 2

u = 5, u = - 2

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 5 : x = 1

Solve

5^{x} = - 2 :

No Solution for

x \in R

x = 1

3^{12 x + 12} = 8 1^{3 x + 3}

x, 4^{5 x + 4} = 3

2^{2 x} - 5 (2^{x}) = - 4

4.7 = 3 (1 + 0.23)^{n}

x, - y = e^{3 x}