PLEASE HELP! Logarithms with x and y's?

Question

Here is my problem:

If log(base a) 2 = x and log(base a) 5 = y, find the terms of x and y, expressions for...

log (base 2) 5

log (base a) 20

Please help me! I don't know where to start. Please teach me how to do this equation.

I am choosing best answer! :)

Thanks You.

Answer 1

You should start from the rules/formulas in your text book. Here are they:

Definition:

f(x) = log (base a) x <===> a^f(x) = x

(x>0, a> 0, and different from 1)

Properties

1. log(base a) uv = log(base a) u + log(base a) v

2. log(base a) u/v = log(base a) u - log(base a) v

3. log(base a) u^n = n log(base a) u

Changing of  base:

log (base b) x = log(base a) x / log(base a) b

Your first question relates to changing of base

Your next question relates to properties 1 and 3 (20= 2^2 * 5)

Answer 2

log (base 2) 5

=(log5)/(log2)

=y/x

log (base a) 20

=(log20)/(loga)

=(2log2+log5)/loga

=(2x+y)/1=2x+y

hint: The base is a for all logs

learn how to change a base of a log

Answer 3

①  log ( base a ) 2 = x  



   it means ,     a^x = 2

   log ( base a ) 5 = y

    it means ,       a^y = 5

    log (base 2) 5

    =  log (base a^x) a^y

    =  y/x log (base a) a

    =  y/x

② log (base a) 20



    = log (base a ) (4x5)  

  

    = log (base a) 4   +   log ( base a ) 5



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



    = 2 log (base a ) 2  + log ( base a )5

    = 2x + y

Answer 4

... log (base 2) 5 ...

CHANGE THE BASE:-

[log (base a) 5] / [log (base a) 2]

= y/x

... log (base a) 20 ...

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

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

= log (base a) 5 + 2 log (base a) 2

= y + 2x

Answer 5

log(base2)5=log(base a)5/log(base a)2=y/x

log(base a)20=log(base a)4 + log(base a)5=2log(base a)2 + log(base a)5

      =2x+y