9^a*3^c= 177,147, 2a+c=x Find the value of x?

Question

9 to the a power times 3 to the c power= 177, 147

Answer 1

9^a * 3^c = 177147
(3^2)^a * 3^c = 177147
3^(2a) * 3^c = 177147
3^(2a + c) = 177147
3^(2a + c) = 3^11

therefore

2a + c = 11

x = 11

Answer 2

9^a3^c = (3^(2a))(3^c) = 3^(2a+c) = 177147 = 3^11
from above
2a+c = 11

2a+c = x
=> x = 11

Answer 3

9 ^a * 3^c = 177,147

take log on both sides (note log a^ b = bloga ; log xy = logx + logy)
alog9 + clog3 = log 177,147
alog (3^2) + clog3 = log177,147
2alog3 + clog3 = log 177,147
2a + c = log177,147/log3 = log (3^11)/log 3 = 11log3/log3 = 11