help me condense this. please?

Question

2(log with base 6 and 15-log with base 6 and 5)+1/2log with base 6 and 1/25

Answer 1

I think that your question is asking me to simplify this:

2 (log(15) - log(5)) + 1/2 log(1 / 25)

where all logs are of base 6.

Using the rule for the subtraction of logs, the equation now becomes:

2 (log(15 / 5)) + 1/2 log(1 / 25)
= 2 log 3 + 1/2 log (1 / 25)

Using the rule: log a ^ b (any base) = b * log a
log (1 / 25) = log (5 ^ (-2)) = -2 * log 5

2 log 3 + 1/2 log (1 / 25)
= 2 log 3 + 1/2 * -2 * log 5
= 2 log 3 - log 5

Using the rule: b * log a = log a ^ b

2 log 3 - log 5
= log (3 ^ 2) - log 5
= log 9 - log 5

Lastly, using the rule of subtraction of logs, we get:

log 9 - log 5
= log (9/ 5).

Unchanged from the beginning of the problem, the base of the logarithms is 6.

Answer 2

2log 15 - log 5 + 1/2log 1/25 (all logs to base 6)
= log225 -log5 +log 1/5
=log225/5*1/5
= log 9

Answer 3

2(log base 6(15/5) times 1/2(log base 6 (1/25)) =
2 log base 6 (3) times 1/2 log base 6 (1/25) =
log base 6 (3^2) times log base 6 (1/25)^1/2 =
log base 6(9) times log base 6(1/5) =
log base 6(9/5)

Answer 4

Uhhhhh uhhhh uhhhhhhhhhh what does condense mean??