if log3(the three is that little number after log)p=m and log3q=2m then log3pq=???

Question

show some solutions please.. need help with this!!!

Answer 1

log(base 3)p = m
log(base 3)q = 2m

log(base 3)pq = m + 2m = 3m.
To find the log of a product, you add the logs of the factors.
As the logs are all to the same base (3), that's all there is to it.

The definition of a logarithm is that if a = b^c, then:
log(base b)a = c.
As logarithms are indices, they follow the rules of indices.
As b^c * b^d = b^(c + d), it follows that:
log(cd) = log(c) + log(d) provided all the logs are to the same base.

Answer 2

log(base 3) p + log(base 3) q = log(base 3) pq

3^m = p
3^(2m) = q

When you multiply powers add the exponents
pq = (3^m)(3^(2m)) = 3^(3m)

log(base 3) pq = 3m
.

Answer 3

log_3(p) = m
log_3(q) = 2m
log_3(pq) = log_3(p) + log_3(q) = 3m

think about what log is. the equation log_3(p) = m means:

3^m = p

similarly, 3^(2m) = q
p*q = 3^m*3^(2m) = 3^(2m+m)
log_3 (p*q) = log_3(3^(3m))

log_x(x^y) = y

so answer is 3m