What is the answer to 5^{3x}=5^{7x-2} ?

The answer to 5^{3x}=5^{7x-2} is x= 1/2

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5^{3x}=5^{7x-2}

5^{3 x} = 5^{7 x - 2}

x = \frac{1}{2}

Decimal

x = 0.5

Solution steps

5^{3 x} = 5^{7 x - 2}

Apply exponent rules

3 x = 7 x - 2

Solve

3 x = 7 x - 2 : x = \frac{1}{2}

x = \frac{1}{2}

2 7^{x - 3} = 8 1^{2 x - 4}

6 e^{4 x - 4} = 42

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

2^{3 - x} = 4^{x}

e^{2 x} + 2 e^{x} - 3 = 0