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# Logarithm?

a) Express log4(x) in terms of log2(x)

b)Express log8(y) in terms of log2(y)

c) Hence solve the simultaneous equations

6log4(x) =3log8(y)=16

log2(x) -2log4(y) =4

### 3 Answers

- VamanLv 72 months ago
a) Express log4(x) in terms of log2(x)

b)Express log8(y) in terms of log2(y)

c) Hence solve the simultaneous equations

6log4(x) =3log8(y)=16

log2(x) -2log4(y) =4

a) Express log4(x) in terms of log2(x), let log 4(x)=y. x= 4^y = 2^(2y) ,

Take log wrt 2. log 4(x)=y, log 2 x= 2y, log 4(x)= 2 log 2 (x)

Similarly, b will have log 8 (y) = 3 log 2 (y).

c) Follow this and write

6 log 4x =12 log 4(y)=16, 3 log 4(x) -6 log4(y)=8.

In terms of base 2, it will be 6 log 2(x) -12 log 2(y)=8

The second equation is log 2x -4 log 2y=4. put log 2(x)= a, and log 2(y)=b

3a-6b=8. a-4b=4, multiply the second equation by 3 and subtract.

12b-6b=4=6b, b=2/3.

a=4*2/3+4=20/3=log2(x), x= 2^(20/3), y= 2^(2/3)

- 2 months ago
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