calculus
posted by Sara .
log (3x9) = 2log3  log27+ log(x+3)
Solving the euqation using the properties of logarithms
How do you do this?

I will assume that all logs have the same base.
log(3x 9) = log [3^2*(x+3)/(3^3]
= log[(x+3)/3]
Therefore
3x 9 = (x+3)/3
9x 27 = x +3
8x = 30
x = 3.75
Check:
log (3x 9) = log 2.25 = 0.35218
2log3 log27 + log(6.75)
= 0.95424 1.43136 + 0.82930
= 0.35218
It makes no difference what log base you choose, as long as it is the same for all terms. (I chose base 10 when checking)