Question

if 8^a=10 b and 2^a=5b then a is equals to

Answer 1

8^a is 10b

So, 2^3a is 10b

or, 2^a is (10b)^1/3

But, 2^a is 5b...

Hence, (10b)^1/3 = 5b

or, 10b is 125b^3

so, b is either 0 or √2/5

When b = 0
2^a is 0
which is not possible...

When b is √2/5
2^a is √2 = 2^-1/2

Hence, a = -1/2


Feel free to ask any doubts