Question

Please find 'x' in the above question

Answer 1

Its easy
(5)^x-3 × (3)^2x-8 = 225
(5)^x-3 × (3)^2x-8 = 5^2 × 3^2
comparing power of both side
first compare power of 5 on bothsides
x-3=2
x= 5
again compare power of 3
2x-8=2
2x=10
x= 5
hope it helps

Answer 2

$5^{x - 3} \times 3^{2x - 8} = 225$

Take out common factor 2:

$5^{x - 3} \times 3^{2(x - 4)} = 225$

Evaluate 3²:

$5^{x - 3} \times 9^{x - 4} = 225$

Apply xᵃ⁻ᵇ = xᵃ/xᵇ:

$\dfrac{5^x}{5^3} \times \dfrac{9^{x}}{9^4}= 5^2 \times 3^2$

Combine into single fraction:

$\dfrac{5^x \times 9^x}{5^3 \times 9^4}= 5^2 \times 3^2$

Apply (aˣ)(bˣ) = (ab)ˣ:

$\dfrac{45^x}{5^3 \times 9^4}= 5^2 \times 3^2$

Cross-multiply:

$45^x= 5^2 \times 3^2 \times 5^3 \times 9^4$

Evaluate 3²:

$45^x= 5^2 \times 9 \times 5^3 \times 9^4$

Apply xᵃ⁺ᵇ = xᵃᵇ:

$45^x= 5^5 \times 9^5$

Apply (aˣ)(bˣ) = (ab)ˣ:

$45^x= 45^5$

Evaluate x:

$x = 5$