What is the answer to 125^x+2(25^x)-3(5^x)=0 ?

The answer to 125^x+2(25^x)-3(5^x)=0 is x=0

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125^x+2(25^x)-3(5^x)=0

12 5^{x} + 2 (2 5^{x}) - 3 (5^{x}) = 0

x = 0

Solution steps

12 5^{x} + 2 (2 5^{x}) - 3 (5^{x}) = 0

Divide both sides by

5^{x}

\frac{12 5 ^{x}}{5 ^{x}} + \frac{2 \cdot 2 5 ^{x}}{5 ^{x}} - \frac{3 \cdot 5 ^{x}}{5 ^{x}} = \frac{0}{5 ^{x}}

Simplify

\frac{12 5 ^{x}}{5 ^{x}} : 2 5^{x}

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

Apply exponent rules

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

Rewrite the equation with

5^{x} = u

(u)^{2} + \frac{2 ( u ) ^{2}}{u} - 3 = 0

Solve

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

u = 1, u = - 3

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 1 : x = 0

Solve

5^{x} = - 3 :

No Solution for

x \in R

x = 0

6^{x} = 2

6^{x} = 0

(3^{x - 1}) (5^{2 x + 1}) = 15

(\frac{1}{8})^{x} = 2

9^{2 x} = 9^{0}

What is the answer to 125^x+2(25^x)-3(5^x)=0 ?
The answer to 125^x+2(25^x)-3(5^x)=0 is x=0
Solve for x: 125^x+2(25^x)-3(5^x)=0
The solution is x=0