Question

if 5 power x-3 * 3 power 2x-8=225. find the value of x.

Answer 1

Hi there !!

Here's your answer

225 can be written in the form of prime factors as :. 3 × 3 × 5 × 5 = 3² × 5²

So,

the equation will be formed which is as follows :


${5}^{x - 3} \times {3}^{2x - 8} = {5}^{2} \times {3}^{2}$
Comparing the value of 5 with 5 and 3 with 3 ,
we have,


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

So,

$x - 3 = 2 \\ x = 3 + 2 \\ x = 5$

also,

$2x - 8 = 2 \\ 2x = 2 + 8 \\ 2x = 10$
$x = \frac{10}{2}$
x = 5

Thus
the value of x is 5

Answer 2

Hi,

Please see the attached file!



Thanks