If $5^{2 x + 1} \div 25 = 125,$ find the value of x.

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Solution

We have $5^{2 x + 1} \div 25 = 125$

Or $\frac{5^{2 x + 1}}{25} = 125$ Or $\frac{5^{2 x + 1}}{5 \times 5} = 5 \times 5 \times 5$

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

Or $5^{2 x - 1} = 5^{3}$
In an equation, when bases on both sides are equal, their powers must also be equal.

Or $2 x - 1 = 3$ Or $2 x = 4$
Or $x = 2$

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