What is the answer to (5^{-2x})/(5^{3x)}=5^{3-x} ?

The answer to (5^{-2x})/(5^{3x)}=5^{3-x} is x=-3/4

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(5^{-2x})/(5^{3x)}=5^{3-x}

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

x = - \frac{3}{4}

Decimal

x = - 0.75

Solution steps

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

Apply exponent rules

- 5 x = 3 - x

Solve

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

x = - \frac{3}{4}

Verify Solutions:

x = - \frac{3}{4}

True

The solution is

x = - \frac{3}{4}

\frac{1}{4} = 6 4^{x}

e^{- x} - x

\frac{100}{e ^{2 x}} = \frac{300}{e ^{4 x}}

5^{2 x} - 2 \times 5^{x} - 15 = 0

5^{x + 3} = 125

What is the answer to (5^{-2x})/(5^{3x)}=5^{3-x} ?
The answer to (5^{-2x})/(5^{3x)}=5^{3-x} is x=-3/4
Solve for x: (5^{-2x})/(5^{3x)}=5^{3-x}
The solution is x=-3/4