Question

If 3^2x-8/225=5^3/5^x, then x=?​

Answer 1

Let's analyze only the terms related with power of 5.

All terms which will be a multiple of 5 will come from 225 and 5³

225 = 25 * 9 = 5² * 9

Let 3^(2x-8) = k. We won't be dealing with this term at all.

Now on rearrangement

∗

5

=

5

3

∗

5

2

∗9

k

∗

5

x

=

5

3

∗

5

2

∗

9

By comparison of powers

5

=

5

3

∗

5

2

=

5

(

2+3)=

5

5

5

x

=

5

3

∗

5

2

=

5

(

2

+

3

)

=

5

5

=5

x

=

5

To cross check you can see that k = 9 = 3²

but k = 3^(2x-8)

So 2x-8=2; 2x = 10 so x=5

In both cases we get the same answer

Hope it helps

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