What is the answer to 25^{x-3}-1/5 =0 ?

The answer to 25^{x-3}-1/5 =0 is x= 5/2

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25^{x-3}-1/5 =0

2 5^{x - 3} - \frac{1}{5} = 0

x = \frac{5}{2}

Decimal Notation

x = 2.5

Solution steps

2 5^{x - 3} - \frac{1}{5} = 0

Add

\frac{1}{5}

to both sides

2 5^{x - 3} - \frac{1}{5} + \frac{1}{5} = 0 + \frac{1}{5}

Simplify

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

Apply exponent rules

2 (x - 3) = - 1

Solve

2 (x - 3) = - 1 : x = \frac{5}{2}

x = \frac{5}{2}

5^{x + 1} + 5^{x - 1} = 130

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

e^{2 x} - e^{x} - 110 = 0

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

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