How do you solve \log _ { 3} ( 7t + 3) - \log _ { 3} t = \log _ { 3} 8?

1 Answer
Aug 15, 2017

t=3

Explanation:

If log_b(mn) = log_b(m) + log_b(n) and

log_b(m/n) = log_b(m) – log_b(n)

So we can write the equation as log_3((7t+3)/t)=log_(3)8

log_3((7t+3)/t) - log_(3)8 = 0

log_3((7t+3)/(t*8))=0

If log_(a)b=0, then b=1

So (7t+3)/(8t)=1

7t+3=8t

giving t=3