Question: Solve: $5^{x-3} × 3^{2x-8} = 225$

Solution:
Given,

$5^{x-3} × 3^{2x-8} = 225$

$or, 5^x × 5^{-3} × 3^{2x} × 3^{-8} = 225$

$or, 5^x × \dfrac{1}{5^3} × 3^{2x} × \dfrac{1}{3^8} = 225$

$or, 5^x × 3^{2x} = (15)² × 5^3 × 3^8$

$or, 5^x × 3^{x+x} = (5^2 × 3^2) × 5^3 × 3^8$

$or, 5^x × 3^x × 3^x = 5^{2+3} × 3^{2+8}$

$or, (5×3×3)^x = 5^5 × 3^{5+5}$

$or, 45^x = 5^5 × 3^5 × 3^5$

$or, 45^x = (5×3×3)^5$

$or, 45^x = 45^5$

$\therefore x=5$
= Answer

Related Notes and Solutions:

Here is the website link to the notes of Indices.

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