Question

find the value of p if 5^p-3×3^2p-8=225

Answer 1

5^p-3  x   3^2p-8  =  5² x  3²

p - 3 = 2

p = 2 + 3 = 5

2p - 8 = 2

2p = 8 +2 = 10

p  10/2 =5

So p = 5

Answer 2

Hey there !

We need to factorize the Right hand side to make it resemble the Left hand side

${5}^{(p - 3)} \times {3}^{(2p - 8)} = 225 \\ \\ {5}^{(p - 3)} \times {3}^{(2p - 8)} = {15}^{2} \\ \\ {5}^{(p - 3)} \times {3}^{(2p - 8)} = {(3 \times 5)}^{2} \\ \\ {5}^{(p - 3)} \times {3}^{(2p - 8)} = {5}^{2} \times {3}^{2}$

Comparing both sides,

p - 3 = 2
=> p = 3 + 2 = 5

2p - 8 = 2
=> 2p = 10
=> p = 5

5 satisfies both values, So p = 5