Question

If \[\frac{3^{2x - 8}}{225} = \frac{5^3}{5^x},\]  then x =

Options

• 2

• 3

• 5

• 4

Answer 1

We have to find the value of x  provided  \[\frac{3^{2x - 8}}{225} = \frac{5^3}{5^x},\]

So,

\[\frac{3^{2x - 8}}{3^2 × 5^2} = \frac{5^3}{5^x}\]

By cross multiplication we get 

`3^(2x-8) xx 5^x = 3^2xx5^2 xx5^3`

By equating exponents we get 

`3^(2x-8) = 3^2`

`2x - 8 = 2`

`2x= 2+8`

`2x = 10`

`x=10/2`

`x=5`

And 

`5^x = 5^(3+2)`

`x=3+2`

`x=5`