Question

solve the following logarithmic equation.
1. 2log(lower2) (x-2) + log(lower2)^2=3
I do not know how to make the 2 by the g on my computer.

2. log(lower729^x) + log(lower27^x) + log(lower3^x) =9
again I do not know how to make the numbers lower case

please show work, and if you can tell me how to make the lower case numbers on here.

Answer 1

lots of folks just write log_2(x-2)
the numbers are subscripts, not lower-case.

1. since we're dealing with logs base 2, just say log:

2log(x-2) + log2 = 3
log(x-2)^2 + log2 = 3
log(2(x-2)^2) = 3
2(x-2)^2 = 8
(x-2)^2 = 4
x = 0 or 4

I assumed that log(lower2)^2 meant log(lower2)2

2.
since 729 = 3^5, log base 729 = 1/5 log base 3
since 27 = 3^3, log base 27 = 1/3 log base 3
so, using all logs base 3,

1/6 logx + 1/3 logx + logx = 9
3/2 logx = 9
logx = 6
x = 3^6 = 729