Question

log 0.5 if log 2= a log 3=b​

Answer 1

Answer:

Let, k=log(25/8)

Hence, k=log(5^2/2^3)

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

k=2*log(5)-3*log(2)

k=2*log(2+3)-3*log(2)

I assume here that ‘e’ is the base of logarithms.

Hence, k=2*log(e^(log(2))+e^(log(3)))-3*log(2)

k=2*log(e^a+e^b)-3*a

If base of logarithm here is ‘10′, then in that case, k=2*log(5)-3*log(2)

k=2*log(10/2)-3*log(2)

k=2*log(10)-2*log(2)-3*log(2)

log(10)=1 if base of logarithm in the question is 10.

k=2-5*log(2) i.e. k=2-5a

There are as many ways as we can find here to represent log(25/8) in terms of ‘a’ and ‘b’ .