If 5^{2x - 1} \times 25^{x + 1} = 125^{x + 2}, what is the value of x? — JAMB UTME

If $5^{2x - 1} \times 25^{x + 1} = 125^{x + 2}$ , what is the value of $x$ ?

Cevap: 5

The value of

x

5

Converting all terms to base

5

gives

5^{2x - 1} \times 5^{2(x + 1)} = 5^{3(x + 2)}

. Simplifying the exponents yields

5^{2x - 1 + 2x + 2} = 5^{3x + 6}

, which reduces to

5^{4x + 1} = 5^{3x + 6}

. Setting the exponents equal to each other gives

4x + 1 = 3x + 6

, resulting in

x = 5

Express all bases in terms of prime base 5

5^{2x - 1} \times (5^2)^{x + 1} = (5^3)^{x + 2}

All terms must share the same base to combine exponents using index laws.

Apply power of a power rule

(a^m)^n = a^{mn}

5^{2x - 1} \times 5^{2x + 2} = 5^{3x + 6}

Multiplication of inner and outer powers simplifies composite exponent expressions.

Apply the product rule

a^m \times a^n = a^{m+n}

5^{4x + 1} = 5^{3x + 6}

Adding the exponents on the left-hand side produces a single exponential term.

Equate exponents and solve for

x

x = 5

Equal bases imply equal exponents:

4x + 1 = 3x + 6

Solving exponential equations using common base conversion and laws of indices

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