What is the answer to 1/((25^x))=125^{3x+2} ?

The answer to 1/((25^x))=125^{3x+2} is x=-6/11

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1/((25^x))=125^{3x+2}

\frac{1}{( 2 5 ^{x} )} = 12 5^{3 x + 2}

x = - \frac{6}{11}

Decimal Notation

x = - 0.54545 \dots

Solution steps

\frac{1}{( 2 5 ^{x} )} = 12 5^{3 x + 2}

Apply exponent rules

- 2 x = 3 (3 x + 2)

Solve

- 2 x = 3 (3 x + 2) : x = - \frac{6}{11}

x = - \frac{6}{11}

Verify Solutions:

x = - \frac{6}{11}

True

The solution is

x = - \frac{6}{11}

2^{x} = \frac{1}{1024}

2^{x} = \frac{4}{9}

2^{x} \cdot 4^{x} = 8^{\frac{1}{3}}

3^{x} + 1 = 4

3 \cdot 2^{x} = 15

What is the answer to 1/((25^x))=125^{3x+2} ?
The answer to 1/((25^x))=125^{3x+2} is x=-6/11
Solve for x: 1/((25^x))=125^{3x+2}
The solution is x=-6/11