Question

Simplify log(base a)1-log(base a)a^b

Answer 1

log(1/(a^b)) => log(a^(-b)) => -blog(a) => -b
sing base is a we have -b

Answer 2

Remember that by definition, for any number x,
$$\log_x 1= 0,$$
since any number to the zeroth power is 1.

Also, remember that, by definition for any number x,
$$\log_x x^b = b.$$
That's what a logarithm is. So combining those two:
$$\log_a 1 - \log_a a^b = 1 - b$$

That's right, the a doesn't matter at all!

Answer 3

Sorry, I that last equation was supposed to read:
$$\log_a 1 - \log_a a^b = -b$$

Answer 4

Rule #1 of posting corrections: your correction will itself contain a mistake. <goes away grumbling darkly/>

Answer 5

thanks, i couldnt put the equation thing.
so the answer is just -b???
that simple?

Answer 6

yes, -b

Answer 7

but you said logx1=0
so shoudltn it be 0-b?

Answer 8

0 is not a "simplification"; it is an overcomplication :)

Answer 9

0 -b = -b ; see :)

Answer 10

ok :)
thanks