What is the answer to 5^{2x}=5^{7x-1} ?

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

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5^{2x}=5^{7x-1}

5^{2 x} = 5^{7 x - 1}

x = \frac{1}{5}

Decimal Notation

x = 0.2

Solution steps

5^{2 x} = 5^{7 x - 1}

Apply exponent rules

2 x = 7 x - 1

Solve

2 x = 7 x - 1 : x = \frac{1}{5}

x = \frac{1}{5}

(0.3)^{1 + x} = 1. 7^{2 x - 1}

4^{2 x - 1} + 4^{2 x} = 4

3 2^{2 x + 3} = 1 6^{x + 4}

3 (2^{2 x + 3}) - 43 (2^{x}) + 5 = 0

2^{2 x + 2} + 2^{x + 2} = 3