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If
5^(2x-1)-100=25^(x-1), then the value of
6^(x).

If $5^{2x-1}-100=25^{x-1}$ , then the value of $6^{x}$ .

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Evaluate expression when a complex numbers and a variable term is given

Full solution

Q. If

5^{2x-1}-100=25^{x-1}

, then the value of

6^{x}

.

Rewrite with Same Base: Rewrite $25$ as $5^2$ to have the same base on both sides of the equation. $\newline$ $25^{(x-1)} = (5^2)^{(x-1)} = 5^{(2x-2)}$ .
Set Equation Equal: Set the equation $5^{2x-1} - 100$ equal to $5^{2x-2}$ . $\newline$ $5^{2x-1} - 100 = 5^{2x-2}.$
Add $100$ to Both Sides: Add $100$ to both sides to isolate the terms with the base $5$ . $\newline$ $5^{(2x-1)} = 5^{(2x-2)} + 100$ .
Set Exponents Equal: Since the bases are the same, set the exponents equal to each other. $2x - 1 = 2x - 2 + 100$ .
Subtract $2x$ : Subtract $2x$ from both sides to get the constants on one side. $-1 = -2 + 100$ .

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