What is the answer to (25^x)/(5^{x+1)}=5^{-3x} ?

The answer to (25^x)/(5^{x+1)}=5^{-3x} is x= 1/4

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(25^x)/(5^{x+1)}=5^{-3x}

\frac{2 5 ^{x}}{5 ^{x + 1}} = 5^{- 3 x}

x = \frac{1}{4}

Decimal Notation

x = 0.25

Solution steps

\frac{2 5 ^{x}}{5 ^{x + 1}} = 5^{- 3 x}

Apply exponent rules

x - 1 = - 3 x

Solve

x - 1 = - 3 x : x = \frac{1}{4}

x = \frac{1}{4}

Verify Solutions:

x = \frac{1}{4}

True

The solution is

x = \frac{1}{4}

(5)^{3 x - 1} = 1

0 = 2 e^{- x} x - e^{- x} x^{2}

3^{2 x} - 2 (3^{x}) - 3 = 0

5^{x + 2} = 25

2^{x + 4} = 16

What is the answer to (25^x)/(5^{x+1)}=5^{-3x} ?
The answer to (25^x)/(5^{x+1)}=5^{-3x} is x= 1/4
Solve for x: (25^x)/(5^{x+1)}=5^{-3x}
The solution is x= 1/4