Question 88625
log7 + log (n - 2) = log 6n
log (7(n - 2)) - log 6n = 0
log (7(n - 2)/6n) = 0
log ((7n - 14)/6n) = 0
(7n - 14)/6n = 10^0 = 1
7n - 14 = 6n
n = 14
{{{graph(500,300,-2,16,-2,4,log(10,7) + log(10,x - 2),log(10,6x))}}}
The main idea is this:
{{{log(10,x) - log(10,x - 1) = log(10,x/(x - 1))}}}
{{{log(10,x) + log(10,x - 1) = log(10,x(x - 1))}}}
I will do two more:
log5m = log5125
5m = 5125
m = 1025
And:
log2(x - 2) + 5 = 8 - log2 4
log2(x - 2) = 3 - log2 2^2
log2(x - 2) = 3 - 2*log2 2
log2(x - 2) = 3 - 2*1
log2(x - 2) = 1
x - 2 = 2^1
x = 4
{{{graph(500,300,-2,6,-2,7,log(2,x - 2) + 5,8 - log(2,4))}}}