Question

Find (x), if
5^(x-3)3^(2x-8)=225


The answer is 5, Need Solution

Solve and become Brainleist​

Answer 1

Answer:

x = 5

Step-by-step explanation:

$Given: 5^{x - 3} \ * \ 3^{2x - 8} = 225$

$\Longrightarrow 5^{x - 3} \ * \ 3^{2x - 8} = 15 * 15$

$\Longrightarrow 5^{x - 3} \ * \ 3^{2x - 8} = 5 * 3 * 5 * 3$

$\Longrightarrow 5^{x - 3} \ * \ 3^{2x - 8} = 5^2 * 3^2$

On comparing both sides, we get

(i)

$\Longrightarrow 5^{x - 3} = 5^2$

$\Longrightarrow x - 3 = 2$

$\Longrightarrow x = 5$

(ii)

$\Longrightarrow 3^{2x - 8} = 3^2$

$\Longrightarrow 2x - 8 = 2$

$\Longrightarrow 2x = 10$

$\Longrightarrow x = 5$

Therefore, the value of x = 5.

Hope it helps!

Answer 2

I think so your question is 5^x-3×3^2x-8=225

5^x-3. 3^2x-8 = 225

We can write 225 as follows:-

225 = 3 × 75

= 3 × 3 × 25

= 3 × 3 × 5 × 5

∴ 5^x-3. 3^2x-8 = 5²×3²

Compare both,

5^x-3=5² | 3^2x-8=3²

Bases are equal exponents must be equal.

x-3=2. | 2x-8=2

x=5. | 2x=10,x=5

Therefore,the value if x is 5