Posted by **confused--two questions please help** on Friday, November 30, 2012 at 2:57pm.

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.

- college algebra -
**Steve**, Friday, November 30, 2012 at 3:24pm
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

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