Logarithm help, Log(base 5)25X?

Question

The answer is 2+log(base5)X. Can somebody explain this please and if they know a website that explains this that would be helpful too, thanks.

Okay nevermind I figured it out, thanks for looking though. IF there is still any good logarithm help sites, could you please put them down, it would be much appreciated.

Answer 1

log[5]25x

=>log[5]25 + log[5] x (since log ab = log a + logb)

=>log[5]5^2 + log[5]x

=>2log[5]5 + log[5]x (since loga^b = b log a)

=>2 + log[5]x (since log of any number to the base of same

number = 1)

Answer 2

Let log be understood as log to base 5 :-
log (25 X) = log 25 + log X
log (25X) = 2 + log X

Answer 3

Remember that when you multiply numbers by one another, you ADD their logs.

For example, Log (base 2) 4 = 2
Log (base 2) 8 = 3
Log (base 2)4X8 = Log(base 2)32 = 5

So you can "take your logs apart" and express them as follows:

Log(base 5)25X = Log(base 5) X + Log(base 5) 25

But
Log(base 5)25 = 2

So the answer is

2 + Log(base 5)X

Answer 4

use the law of log addition

Log nm = log m + log n

log25x = log 25 + log x

log (base 5)25 = log (base 5) 5^2

use the law of log muliplication

Log m^n = n log m

log(base 5)5^2 = 2 log(base 5)5

log(base 5)5 = 1 so that is your ans.

Answer 5

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