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.

#SciPiPupil