What is the answer to 3x(10^x)+10^x=0 ?

The answer to 3x(10^x)+10^x=0 is x=-1/3

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3x(10^x)+10^x=0

3 x (1 0^{x}) + 1 0^{x} = 0

x = - \frac{1}{3}

Decimal Notation

x = - 0.33333 \dots

Solution steps

3 x (1 0^{x}) + 1 0^{x} = 0

Factor

3 x \cdot 1 0^{x} + 1 0^{x} : 1 0^{x} (3 x + 1)

1 0^{x} (3 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

1 0^{x} = 0 or 3 x + 1 = 0

Solve

1 0^{x} = 0 :

No Solution for

x \in R

Solve

3 x + 1 = 0 : x = - \frac{1}{3}

x = - \frac{1}{3}

3^{2 z} = 81

2^{3 y - 2} = 16

2^{2 x - 3} = 8^{x + 1}

2^{x} = 5^{x}

9^{x - 1} = 2 7^{3 x + 4}